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2\left(x^{2}-4x-12\right)
Factor out 2.
a+b=-4 ab=1\left(-12\right)=-12
Consider x^{2}-4x-12. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-12. 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(x^{2}-6x\right)+\left(2x-12\right)
Rewrite x^{2}-4x-12 as \left(x^{2}-6x\right)+\left(2x-12\right).
x\left(x-6\right)+2\left(x-6\right)
Factor out x in the first and 2 in the second group.
\left(x-6\right)\left(x+2\right)
Factor out common term x-6 by using distributive property.
2\left(x-6\right)\left(x+2\right)
Rewrite the complete factored expression.
2x^{2}-8x-24=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 2\left(-24\right)}}{2\times 2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-\left(-8\right)±\sqrt{64-4\times 2\left(-24\right)}}{2\times 2}
Square -8.
x=\frac{-\left(-8\right)±\sqrt{64-8\left(-24\right)}}{2\times 2}
Multiply -4 times 2.
x=\frac{-\left(-8\right)±\sqrt{64+192}}{2\times 2}
Multiply -8 times -24.
x=\frac{-\left(-8\right)±\sqrt{256}}{2\times 2}
Add 64 to 192.
x=\frac{-\left(-8\right)±16}{2\times 2}
Take the square root of 256.
x=\frac{8±16}{2\times 2}
The opposite of -8 is 8.
x=\frac{8±16}{4}
Multiply 2 times 2.
x=\frac{24}{4}
Now solve the equation x=\frac{8±16}{4} when ± is plus. Add 8 to 16.
x=6
Divide 24 by 4.
x=\frac{-8}{4}
Now solve the equation x=\frac{8±16}{4} when ± is minus. Subtract 16 from 8.
x=-2
Divide -8 by 4.
2x^{2}-8x-24=2\left(x-6\right)\left(x-\left(-2\right)\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 6 for x_{1} and -2 for x_{2}.
2x^{2}-8x-24=2\left(x-6\right)\left(x+2\right)
Simplify all the expressions of the form p-\left(-q\right) to p+q.