Solve (3+.2x)(x-15)=5left(6-.2xright)^2

$$(3+.2x)(x-15)=5 { \left(6-.2x \right) }^{ 2 }$$

Solve for x

$$x=18.75$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3+0.2x by x-15 and combine like terms.

$$-45+0.2x^{2}=5\left(6-0.2x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6-0.2x\right)^{2}.

$$-45+0.2x^{2}=5\left(36-2.4x+0.04x^{2}\right)$$

Use the distributive property to multiply 5 by 36-2.4x+0.04x^{2}.

$$-45+0.2x^{2}=180-12x+0.2x^{2}$$

Add 12x to both sides.

$$-45+0.2x^{2}+12x=180+0.2x^{2}$$

Subtract 0.2x^{2} from both sides.

$$-45+0.2x^{2}+12x-0.2x^{2}=180$$

Combine 0.2x^{2} and -0.2x^{2} to get 0.

$$-45+12x=180$$

Add 45 to both sides.

$$12x=180+45$$

Add 180 and 45 to get 225.

$$12x=225$$

Divide both sides by 12.

$$x=\frac{225}{12}$$

Reduce the fraction \frac{225}{12} to lowest terms by extracting and canceling out 3.

$$x=\frac{75}{4}$$