(x-2)(x+3)=66

Solution for (x-2)(x+3)=66 equation:

Simplifying
(x + -2)(x + 3) = 66

Reorder the terms:
(-2 + x)(x + 3) = 66

Reorder the terms:
(-2 + x)(3 + x) = 66

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) = 66
((3 * -2 + x * -2) + x(3 + x)) = 66
((-6 + -2x) + x(3 + x)) = 66
(-6 + -2x + (3 * x + x * x)) = 66
(-6 + -2x + (3x + x2)) = 66

Combine like terms: -2x + 3x = 1x
(-6 + 1x + x2) = 66

Solving
-6 + 1x + x2 = 66

Solving for variable 'x'.

Reorder the terms:
-6 + -66 + 1x + x2 = 66 + -66

Combine like terms: -6 + -66 = -72
-72 + 1x + x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-72 + 1x + x2 = 0

Factor a trinomial.
(-9 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-9, 8}