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6\left(6x^{3}-5x^{2}-6x\right)
Factor out 6.
x\left(6x^{2}-5x-6\right)
Consider 6x^{3}-5x^{2}-6x. Factor out x.
a+b=-5 ab=6\left(-6\right)=-36
Consider 6x^{2}-5x-6. Factor the expression by grouping. First, the expression needs to be rewritten as 6x^{2}+ax+bx-6. To find a and b, set up a system to be solved.
1,-36 2,-18 3,-12 4,-9 6,-6
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 -36.
1-36=-35 2-18=-16 3-12=-9 4-9=-5 6-6=0
Calculate the sum for each pair.
a=-9 b=4
The solution is the pair that gives sum -5.
\left(6x^{2}-9x\right)+\left(4x-6\right)
Rewrite 6x^{2}-5x-6 as \left(6x^{2}-9x\right)+\left(4x-6\right).
3x\left(2x-3\right)+2\left(2x-3\right)
Factor out 3x in the first and 2 in the second group.
\left(2x-3\right)\left(3x+2\right)
Factor out common term 2x-3 by using distributive property.
6x\left(2x-3\right)\left(3x+2\right)
Rewrite the complete factored expression.