(x-4)(x+3)=-12

Solution for (x-4)(x+3)=-12 equation:

Simplifying
(x + -4)(x + 3) = -12

Reorder the terms:
(-4 + x)(x + 3) = -12

Reorder the terms:
(-4 + x)(3 + x) = -12

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

Combine like terms: -4x + 3x = -1x
(-12 + -1x + x2) = -12

Add '12' to each side of the equation.
-12 + -1x + 12 + x2 = -12 + 12

Reorder the terms:
-12 + 12 + -1x + x2 = -12 + 12

Combine like terms: -12 + 12 = 0
0 + -1x + x2 = -12 + 12
-1x + x2 = -12 + 12

Combine like terms: -12 + 12 = 0
-1x + x2 = 0

Solving
-1x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}