(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

Solving
-6 + -1x + x2 = 6

Solving for variable 'x'.

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

Combine like terms: -6 + -6 = -12
-12 + -1x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-12 + -1x + x2 = 0

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

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 + -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
Solution
x = {-3, 4}