=2(x+3)(x-4)

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Solution for =2(x+3)(x-4) equation: 


Simplifying
0 = 2(x + 3)(x + -4)

Reorder the terms:
0 = 2(3 + x)(x + -4)

Reorder the terms:
0 = 2(3 + x)(-4 + x)

Multiply (3 + x) * (-4 + x)
0 = 2(3(-4 + x) + x(-4 + x))
0 = 2((-4 * 3 + x * 3) + x(-4 + x))
0 = 2((-12 + 3x) + x(-4 + x))
0 = 2(-12 + 3x + (-4 * x + x * x))
0 = 2(-12 + 3x + (-4x + x2))

Combine like terms: 3x + -4x = -1x
0 = 2(-12 + -1x + x2)
0 = (-12 * 2 + -1x * 2 + x2 * 2)
0 = (-24 + -2x + 2x2)

Solving
0 = -24 + -2x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 24 = 24
24 + 2x + -2x2 = -24 + -2x + 2x2 + 24 + 2x + -2x2

Reorder the terms:
24 + 2x + -2x2 = -24 + 24 + -2x + 2x + 2x2 + -2x2

Combine like terms: -24 + 24 = 0
24 + 2x + -2x2 = 0 + -2x + 2x + 2x2 + -2x2
24 + 2x + -2x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
24 + 2x + -2x2 = 0 + 2x2 + -2x2
24 + 2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
24 + 2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + x + -1x2) = 0

Factor a trinomial.
2((4 + -1x)(3 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {4, -3}

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