Solve 4x ^ 2 + 8x - 60 = c; )(x-3)6 alpha+5 | 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

$$4x^{2}+8x-60=c; )(x-3)6\alpha+5$$

Solve for c

$c=-\frac{4\left(6x^{2}+2x-15\right)}{x\left(15-2x-x^{2}\right)}$
$x\neq -5\text{ and }x\neq 3\text{ and }x\neq 0$

Steps for Solving Linear Equation

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

$$24x^{2}+8x-60=\left(cx^{2}-3cx\right)\left(x+5\right)$$

Use the distributive property to multiply $cx^{2}-3cx$ by $x+5$ and combine like terms.

$$24x^{2}+8x-60=cx^{3}+2cx^{2}-15xc$$

Swap sides so that all variable terms are on the left hand side.

$$cx^{3}+2cx^{2}-15xc=24x^{2}+8x-60$$

Combine all terms containing $c$.

$$\left(x^{3}+2x^{2}-15x\right)c=24x^{2}+8x-60$$

Divide both sides by $x^{3}+2x^{2}-15x$.

$$\frac{\left(x^{3}+2x^{2}-15x\right)c}{x^{3}+2x^{2}-15x}=\frac{24x^{2}+8x-60}{x^{3}+2x^{2}-15x}$$

Dividing by $x^{3}+2x^{2}-15x$ undoes the multiplication by $x^{3}+2x^{2}-15x$.

$$c=\frac{24x^{2}+8x-60}{x^{3}+2x^{2}-15x}$$

Divide $24x^{2}+8x-60$ by $x^{3}+2x^{2}-15x$.

$$c=\frac{4\left(6x^{2}+2x-15\right)}{x\left(x^{2}+2x-15\right)}$$