(x+2)(x-3)=-6

Solution for (x+2)(x-3)=-6 equation:

Simplifying
(x + 2)(x + -3) = -6

Reorder the terms:
(2 + x)(x + -3) = -6

Reorder the terms:
(2 + x)(-3 + x) = -6

Multiply (2 + x) * (-3 + x)
(2(-3 + x) + x(-3 + x)) = -6
((-3 * 2 + x * 2) + x(-3 + x)) = -6
((-6 + 2x) + x(-3 + x)) = -6
(-6 + 2x + (-3 * x + x * x)) = -6
(-6 + 2x + (-3x + x2)) = -6

Combine like terms: 2x + -3x = -1x
(-6 + -1x + x2) = -6

Add '6' to each side of the equation.
-6 + -1x + 6 + x2 = -6 + 6

Reorder the terms:
-6 + 6 + -1x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
0 + -1x + x2 = -6 + 6
-1x + x2 = -6 + 6

Combine like terms: -6 + 6 = 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}