Solve (2n)/3 * (- 3n)/8 = 7/12 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{2n}{3}\frac{-3n}{8}=\frac{7}{12}$$

Solve for n

$n=-\frac{\sqrt{21}i}{3}\approx -0-1.527525232i$
$n=\frac{\sqrt{21}i}{3}\approx 1.527525232i$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Multiply both sides of the equation by $24$, the least common multiple of $3,8,12$.

$$2n\left(-3\right)n=14$$

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

$$-6nn=14$$

Multiply $n$ and $n$ to get $n^{2}$.

$$-6n^{2}=14$$

Divide both sides by $-6$.

$$n^{2}=\frac{14}{-6}$$

Reduce the fraction $\frac{14}{-6}$ to lowest terms by extracting and canceling out $2$.

$$n^{2}=-\frac{7}{3}$$

The equation is now solved.

$$n=\frac{\sqrt{21}i}{3}$$ $$n=-\frac{\sqrt{21}i}{3}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by $24$, the least common multiple of $3,8,12$.

$$2n\left(-3\right)n=14$$

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

$$-6nn=14$$

Multiply $n$ and $n$ to get $n^{2}$.

$$-6n^{2}=14$$

Subtract $14$ from both sides.

$$-6n^{2}-14=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-6$ for $a$, $0$ for $b$, and $-14$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$n=\frac{0±\sqrt{0^{2}-4\left(-6\right)\left(-14\right)}}{2\left(-6\right)}$$

Square $0$.

$$n=\frac{0±\sqrt{-4\left(-6\right)\left(-14\right)}}{2\left(-6\right)}$$

Multiply $-4$ times $-6$.

$$n=\frac{0±\sqrt{24\left(-14\right)}}{2\left(-6\right)}$$

Multiply $24$ times $-14$.

$$n=\frac{0±\sqrt{-336}}{2\left(-6\right)}$$

Take the square root of $-336$.

$$n=\frac{0±4\sqrt{21}i}{2\left(-6\right)}$$

Multiply $2$ times $-6$.

$$n=\frac{0±4\sqrt{21}i}{-12}$$

Now solve the equation $n=\frac{0±4\sqrt{21}i}{-12}$ when $±$ is plus.

$$n=-\frac{\sqrt{21}i}{3}$$

Now solve the equation $n=\frac{0±4\sqrt{21}i}{-12}$ when $±$ is minus.

$$n=\frac{\sqrt{21}i}{3}$$

The equation is now solved.

$$n=-\frac{\sqrt{21}i}{3}$$ $$n=\frac{\sqrt{21}i}{3}$$