Answer
$x=-\frac{3}{2}$ and $x=\frac{3}{2}$.
Work Step by Step
The given polynomial is
$\Rightarrow 16x^2-36=0$
Factor out $4$.
$\Rightarrow 4(4x^2-9)=0$
$\Rightarrow 4(2^2x^2-3^2)=0$
Write the the polynomial as $a^2-b^2$.
$\Rightarrow 4[(2x)^2-(3)^2]=0$
Use difference of two square pattern
$a^2-b^2=(a+b)(a-b)$
We have $a=2x$ and $b=3$.
$\Rightarrow 4(2x+3)(2x-3)=0$
Use zero product property.
$\Rightarrow 2x+3=0$ or $2x-3=0$
Solve for $x$.
$\Rightarrow x=-\frac{3}{2}$ or $x=\frac{3}{2}$
Hence, the solutions are $x=-\frac{3}{2}$ and $x=\frac{3}{2}$.
