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5\left(4xy^{2}-4xy-3x\right)
Factor out 5.
x\left(4y^{2}-4y-3\right)
Consider 4xy^{2}-4xy-3x. Factor out x.
a+b=-4 ab=4\left(-3\right)=-12
Consider 4y^{2}-4y-3. Factor the expression by grouping. First, the expression needs to be rewritten as 4y^{2}+ay+by-3. To find a and b, set up a system to be solved.
1,-12 2,-6 3,-4
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -12.
1-12=-11 2-6=-4 3-4=-1
Calculate the sum for each pair.
a=-6 b=2
The solution is the pair that gives sum -4.
\left(4y^{2}-6y\right)+\left(2y-3\right)
Rewrite 4y^{2}-4y-3 as \left(4y^{2}-6y\right)+\left(2y-3\right).
2y\left(2y-3\right)+2y-3
Factor out 2y in 4y^{2}-6y.
\left(2y-3\right)\left(2y+1\right)
Factor out common term 2y-3 by using distributive property.
5x\left(2y-3\right)\left(2y+1\right)
Rewrite the complete factored expression.