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

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

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

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

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

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

Combine like terms: 3x + -2x = 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.
(-4 + -1x)(3 + -1x) = 0

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 + -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
Solution
x = {-4, 3}