How to solve 3x 6x - 6x

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 3x 6x - 6x | Equatix

Question

$$3 x ( 6 x - 8 ) = 6 x$$

Solve for x

$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$
$x=0$

Steps Using Factoring

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using Factoring

Use the distributive property to multiply $3x$ by $6x-8$.

$$18x^{2}-24x=6x$$

Subtract $6x$ from both sides.

$$18x^{2}-24x-6x=0$$

Combine $-24x$ and $-6x$ to get $-30x$.

$$18x^{2}-30x=0$$

Factor out $x$.

$$x\left(18x-30\right)=0$$

To find equation solutions, solve $x=0$ and $18x-30=0$.

$$x=0$$ $$x=\frac{5}{3}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply $3x$ by $6x-8$.

$$18x^{2}-24x=6x$$

Subtract $6x$ from both sides.

$$18x^{2}-24x-6x=0$$

Combine $-24x$ and $-6x$ to get $-30x$.

$$18x^{2}-30x=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $18$ for $a$, $-30$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{-\left(-30\right)±\sqrt{\left(-30\right)^{2}}}{2\times 18}$$

Take the square root of $\left(-30\right)^{2}$.

$$x=\frac{-\left(-30\right)±30}{2\times 18}$$

The opposite of $-30$ is $30$.

$$x=\frac{30±30}{2\times 18}$$

Multiply $2$ times $18$.

$$x=\frac{30±30}{36}$$

Now solve the equation $x=\frac{30±30}{36}$ when $±$ is plus. Add $30$ to $30$.

$$x=\frac{60}{36}$$

Reduce the fraction $\frac{60}{36}$ to lowest terms by extracting and canceling out $12$.

$$x=\frac{5}{3}$$

Now solve the equation $x=\frac{30±30}{36}$ when $±$ is minus. Subtract $30$ from $30$.

$$x=\frac{0}{36}$$

Divide $0$ by $36$.

$$x=0$$

The equation is now solved.

$$x=\frac{5}{3}$$ $$x=0$$

Steps for Completing the Square

Use the distributive property to multiply $3x$ by $6x-8$.

$$18x^{2}-24x=6x$$

Subtract $6x$ from both sides.

$$18x^{2}-24x-6x=0$$

Combine $-24x$ and $-6x$ to get $-30x$.

$$18x^{2}-30x=0$$

Divide both sides by $18$.

$$\frac{18x^{2}-30x}{18}=\frac{0}{18}$$

Dividing by $18$ undoes the multiplication by $18$.

$$x^{2}+\left(-\frac{30}{18}\right)x=\frac{0}{18}$$

Reduce the fraction $\frac{-30}{18}$ to lowest terms by extracting and canceling out $6$.

$$x^{2}-\frac{5}{3}x=\frac{0}{18}$$

Divide $0$ by $18$.

$$x^{2}-\frac{5}{3}x=0$$

Divide $-\frac{5}{3}$, the coefficient of the $x$ term, by $2$ to get $-\frac{5}{6}$. Then add the square of $-\frac{5}{6}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{5}{3}x+\left(-\frac{5}{6}\right)^{2}=\left(-\frac{5}{6}\right)^{2}$$

Square $-\frac{5}{6}$ by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{5}{3}x+\frac{25}{36}=\frac{25}{36}$$

Factor $x^{2}-\frac{5}{3}x+\frac{25}{36}$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.

$$\left(x-\frac{5}{6}\right)^{2}=\frac{25}{36}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{5}{6}\right)^{2}}=\sqrt{\frac{25}{36}}$$

Simplify.

$$x-\frac{5}{6}=\frac{5}{6}$$ $$x-\frac{5}{6}=-\frac{5}{6}$$

Add $\frac{5}{6}$ to both sides of the equation.

$$x=\frac{5}{3}$$ $$x=0$$

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Example

Question

Solve for x

Steps Using Factoring

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using Factoring

Steps Using the Quadratic Formula

Steps for Completing the Square