How to solve 2x + 1 ) 6

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 2x + 1 ) 6 | Equatix

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Question

$$\frac { ( 2 x + 1 ) ^ { 2 } } { 4 } - \frac { 3 ( x - 2 ) ^ { 2 } } { 6 } = \frac { x ( x - 2 ) } { 2 }$$

Solve for x

$x=\frac{7}{16}=0.4375$

Steps for Solving Linear Equation

Multiply both sides of the equation by $12$, the least common multiple of $4,6,2$.

$$3\left(2x+1\right)^{2}-2\times 3\left(x-2\right)^{2}=6x\left(x-2\right)$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(2x+1\right)^{2}$.

$$3\left(4x^{2}+4x+1\right)-2\times 3\left(x-2\right)^{2}=6x\left(x-2\right)$$

Use the distributive property to multiply $3$ by $4x^{2}+4x+1$.

$$12x^{2}+12x+3-2\times 3\left(x-2\right)^{2}=6x\left(x-2\right)$$

Multiply $-2$ and $3$ to get $-6$.

$$12x^{2}+12x+3-6\left(x-2\right)^{2}=6x\left(x-2\right)$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-2\right)^{2}$.

$$12x^{2}+12x+3-6\left(x^{2}-4x+4\right)=6x\left(x-2\right)$$

Use the distributive property to multiply $-6$ by $x^{2}-4x+4$.

$$12x^{2}+12x+3-6x^{2}+24x-24=6x\left(x-2\right)$$

Combine $12x^{2}$ and $-6x^{2}$ to get $6x^{2}$.

$$6x^{2}+12x+3+24x-24=6x\left(x-2\right)$$

Combine $12x$ and $24x$ to get $36x$.

$$6x^{2}+36x+3-24=6x\left(x-2\right)$$

Subtract $24$ from $3$ to get $-21$.

$$6x^{2}+36x-21=6x\left(x-2\right)$$

Use the distributive property to multiply $6x$ by $x-2$.

$$6x^{2}+36x-21=6x^{2}-12x$$

Subtract $6x^{2}$ from both sides.

$$6x^{2}+36x-21-6x^{2}=-12x$$

Combine $6x^{2}$ and $-6x^{2}$ to get $0$.

$$36x-21=-12x$$

Add $12x$ to both sides.

$$36x-21+12x=0$$

Combine $36x$ and $12x$ to get $48x$.

$$48x-21=0$$

Add $21$ to both sides. Anything plus zero gives itself.

$$48x=21$$

Divide both sides by $48$.

$$x=\frac{21}{48}$$

Reduce the fraction $\frac{21}{48}$ to lowest terms by extracting and canceling out $3$.

$$x=\frac{7}{16}$$

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