# Solve the following polynomial equation by grouping and factoring. 4y^3−9y=0 y=?

Solve the following polynomial equation by grouping and factoring.
$4{y}^{3}-9y=0$
y=?
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Step 1
Given a polynomial equation,
$4{y}^{3}-9y=0$
Step 2
Now to solve the polynomial,
By using the factorization method,
$y\left(4{y}^{2}-9\right)=0$
Now, by the formula of the square of difference,
${x}^{2}-{y}^{2}=\left(x-y\right)\left(x+y\right)$
Thus,
$⇒y\left(2y+3\right)\left(2y-3\right)=0$
Step 3
Now, by zeros factorization principle,
If ab=0 then a=0 or b=0,
$⇒y=0$ or (2y+3)=0 or (2y-3)=0
Thus,
$⇒2y+3=0$
$⇒y=-\frac{3}{2}$
And
$⇒2y-3=0$
$⇒y=\frac{3}{2}$
Step 4
Therefore, the solution of the polynomial is
y=0 or $y=-\frac{3}{2}\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}y=\frac{3}{2}$
$y=0,-\frac{3}{2},\frac{3}{2}$.