Solve (2u+1)^2-2(u-2)(u+2)=2u^2+9

$$( 2 u + 1 ) ^ { 2 } - 2 ( u - 2 ) ( u + 2 ) = 2 u ^ { 2 } + 9$$

Solve for u

$$u=0$$

Steps for Solving Linear Equation

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

$$4u^{2}+4u+1-2\left(u-2\right)\left(u+2\right)=2u^{2}+9$$

Subtract 2u^{2} from both sides.

$$4u^{2}+4u+1-2\left(u-2\right)\left(u+2\right)-2u^{2}=9$$

Use the distributive property to multiply -2 by u-2.

$$4u^{2}+4u+1+\left(-2u+4\right)\left(u+2\right)-2u^{2}=9$$

Use the distributive property to multiply -2u+4 by u+2 and combine like terms.

$$4u^{2}+4u+1-2u^{2}+8-2u^{2}=9$$

Combine 4u^{2} and -2u^{2} to get 2u^{2}.

$$2u^{2}+4u+1+8-2u^{2}=9$$

Add 1 and 8 to get 9.

$$2u^{2}+4u+9-2u^{2}=9$$

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

$$4u+9=9$$

Subtract 9 from both sides.

$$4u=9-9$$

Subtract 9 from 9 to get 0.

$$4u=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 4 is not equal to 0, u must be equal to 0.

$$u=0$$