Solve 9x^2-1=left(3x-2right)^2

$$9 { x }^{ 2 } -1= { \left(3x-2 \right) }^{ 2 }$$

Solve for x

$$x=\frac{5}{12}\approx 0.416666667$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2\right)^{2}.

$$9x^{2}-1=9x^{2}-12x+4$$

Subtract 9x^{2} from both sides.

$$9x^{2}-1-9x^{2}=-12x+4$$

Combine 9x^{2} and -9x^{2} to get 0.

$$-1=-12x+4$$

Swap sides so that all variable terms are on the left hand side.

$$-12x+4=-1$$

Subtract 4 from both sides.

$$-12x=-1-4$$

Subtract 4 from -1 to get -5.

$$-12x=-5$$

Divide both sides by -12.

$$x=\frac{-5}{-12}$$

Fraction \frac{-5}{-12} can be simplified to \frac{5}{12} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{12}$$