Solve left(x+10right)^2=xleft(x+40right)

$${ \left(x+10 \right) }^{ 2 } = x \left( x+40 \right)$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+10\right)^{2}.

$$x^{2}+20x+100=x\left(x+40\right)$$

Use the distributive property to multiply x by x+40.

$$x^{2}+20x+100=x^{2}+40x$$

Subtract x^{2} from both sides.

$$x^{2}+20x+100-x^{2}=40x$$

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

$$20x+100=40x$$

Subtract 40x from both sides.

$$20x+100-40x=0$$

Combine 20x and -40x to get -20x.

$$-20x+100=0$$

Subtract 100 from both sides. Anything subtracted from zero gives its negation.

$$-20x=-100$$

Divide both sides by -20.

$$x=\frac{-100}{-20}$$

Divide -100 by -20 to get 5.

$$x=5$$