Solve 3(h-2)^2(h+5)=3(h+1)^2(h-1)+3

$$3 ( h - 2 ) ^ { 2 } ( h + 5 ) = 3 ( h + 1 ) ^ { 2 } ( h - 1 ) + 3$$

Solve for h

$$h = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Steps for Solving Linear Equation

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

$$3\left(h^{2}-4h+4\right)\left(h+5\right)=3\left(h+1\right)^{2}\left(h-1\right)+3$$

Use the distributive property to multiply 3 by h^{2}-4h+4.

$$\left(3h^{2}-12h+12\right)\left(h+5\right)=3\left(h+1\right)^{2}\left(h-1\right)+3$$

Use the distributive property to multiply 3h^{2}-12h+12 by h+5 and combine like terms.

$$3h^{3}+3h^{2}-48h+60=3\left(h+1\right)^{2}\left(h-1\right)+3$$

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

$$3h^{3}+3h^{2}-48h+60=3\left(h^{2}+2h+1\right)\left(h-1\right)+3$$

Use the distributive property to multiply 3 by h^{2}+2h+1.

$$3h^{3}+3h^{2}-48h+60=\left(3h^{2}+6h+3\right)\left(h-1\right)+3$$

Use the distributive property to multiply 3h^{2}+6h+3 by h-1 and combine like terms.

$$3h^{3}+3h^{2}-48h+60=3h^{3}+3h^{2}-3h-3+3$$

Add -3 and 3 to get 0.

$$3h^{3}+3h^{2}-48h+60=3h^{3}+3h^{2}-3h$$

Subtract 3h^{3} from both sides.

$$3h^{3}+3h^{2}-48h+60-3h^{3}=3h^{2}-3h$$

Combine 3h^{3} and -3h^{3} to get 0.

$$3h^{2}-48h+60=3h^{2}-3h$$

Subtract 3h^{2} from both sides.

$$3h^{2}-48h+60-3h^{2}=-3h$$

Combine 3h^{2} and -3h^{2} to get 0.

$$-48h+60=-3h$$

Add 3h to both sides.

$$-48h+60+3h=0$$

Combine -48h and 3h to get -45h.

$$-45h+60=0$$

Subtract 60 from both sides. Anything subtracted from zero gives its negation.

$$-45h=-60$$

Divide both sides by -45.

$$h=\frac{-60}{-45}$$

Reduce the fraction \frac{-60}{-45} to lowest terms by extracting and canceling out -15.

$$h=\frac{4}{3}$$