(x-2)(x+3)-6=0

Solution for (x-2)(x+3)-6=0 equation:

Simplifying
(x + -2)(x + 3) + -6 = 0

Reorder the terms:
(-2 + x)(x + 3) + -6 = 0

Reorder the terms:
(-2 + x)(3 + x) + -6 = 0

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) + -6 = 0
((3 * -2 + x * -2) + x(3 + x)) + -6 = 0
((-6 + -2x) + x(3 + x)) + -6 = 0
(-6 + -2x + (3 * x + x * x)) + -6 = 0
(-6 + -2x + (3x + x2)) + -6 = 0

Combine like terms: -2x + 3x = 1x
(-6 + 1x + x2) + -6 = 0

Reorder the terms:
-6 + -6 + 1x + x2 = 0

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

Solving
-12 + 1x + x2 = 0

Solving for variable 'x'.

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}