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

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Solution for 0=2(x+4)(x-3) equation: 


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

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

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

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

Combine like terms: 4x + -3x = 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 + -1x + -1x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

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

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