Solve 4x^2+9=left(9-2xright)^2

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(9-2x\right)^{2}.

$$4x^{2}+9=81-36x+4x^{2}$$

Add 36x to both sides.

$$4x^{2}+9+36x=81+4x^{2}$$

Subtract 4x^{2} from both sides.

$$4x^{2}+9+36x-4x^{2}=81$$

Combine 4x^{2} and -4x^{2} to get 0.

$$9+36x=81$$

Subtract 9 from both sides.

$$36x=81-9$$

Subtract 9 from 81 to get 72.

$$36x=72$$

Divide both sides by 36.

$$x=\frac{72}{36}$$

Divide 72 by 36 to get 2.

$$x=2$$