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

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

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

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

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

Multiply (-4 + x) * (3 + x)
-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)) = 0

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

Solving
24 + 2x + -2x2 = 0

Solving for variable 'x'.

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}