Solve (6x-5)^2=9(2x+1)^2

$$( 6 x - 5 ) ^ { 2 } = 9 ( 2 x + 1 ) ^ { 2 }$$

Solve for x

$$x=\frac{1}{6}\approx 0.166666667$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6x-5\right)^{2}.

$$36x^{2}-60x+25=9\left(2x+1\right)^{2}$$

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

$$36x^{2}-60x+25=9\left(4x^{2}+4x+1\right)$$

Use the distributive property to multiply 9 by 4x^{2}+4x+1.

$$36x^{2}-60x+25=36x^{2}+36x+9$$

Subtract 36x^{2} from both sides.

$$36x^{2}-60x+25-36x^{2}=36x+9$$

Combine 36x^{2} and -36x^{2} to get 0.

$$-60x+25=36x+9$$

Subtract 36x from both sides.

$$-60x+25-36x=9$$

Combine -60x and -36x to get -96x.

$$-96x+25=9$$

Subtract 25 from both sides.

$$-96x=9-25$$

Subtract 25 from 9 to get -16.

$$-96x=-16$$

Divide both sides by -96.

$$x=\frac{-16}{-96}$$

Reduce the fraction \frac{-16}{-96} to lowest terms by extracting and canceling out -16.

$$x=\frac{1}{6}$$