Factor completely and solve $$ 16 x^{2}-36 $$

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Factor the expression $$ 16x^2-36 $$.
Factor the expression by following steps:
- step0: Factor:
  $$16x^{2}-36$$
- step1: Factor the expression:
  $$4\left(4x^{2}-9ight)$$
- step2: Factor the expression:
  $$4\left(2x-3ight)\left(2x+3ight)$$
Solve the equation $$ 4(2x-3)(2x+3) = 0 $$.
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
  $$4\left(2x-3ight)\left(2x+3ight)=0$$
- step1: Divide both sides:
  $$\left(2x-3ight)\left(2x+3ight)=0$$
- step2: Expand the expression:
  $$4x^{2}-9=0$$
- step3: Add or subtract both sides:
  $$4x^{2}=9$$
- step4: Divide both sides:
  $$\frac{4x^{2}}{4}=\frac{9}{4}$$
- step5: Divide the numbers:
  $$x^{2}=\frac{9}{4}$$
- step6: Simplify the expression:
  $$x=\pm \sqrt{\frac{9}{4}}$$
- step7: Simplify the expression:
  $$x=\pm \frac{3}{2}$$
- step8: Separate into possible cases:
  $$\begin{align}&x=\frac{3}{2}\&x=-\frac{3}{2}\end{align}$$
- step9: Rewrite:
  $$x_{1}=-\frac{3}{2},x_{2}=\frac{3}{2}$$
The factored form of the expression $$16x^2 - 36$$ is $$4(2x-3)(2x+3)$$.

The solutions to the equation $$4(2x-3)(2x+3) = 0$$ are $$x = -\frac{3}{2}$$ and $$x = \frac{3}{2}$$.
The expression $$16x^2 - 36$$ factors to $$4(2x - 3)(2x + 3)$$. The solutions are $$x = -\frac{3}{2}$$ and $$x = \frac{3}{2}$$.

Factor completely and solve

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