(x-2)(x+6)=33

Solution for (x-2)(x+6)=33 equation:

Simplifying
(x + -2)(x + 6) = 33

Reorder the terms:
(-2 + x)(x + 6) = 33

Reorder the terms:
(-2 + x)(6 + x) = 33

Multiply (-2 + x) * (6 + x)
(-2(6 + x) + x(6 + x)) = 33
((6 * -2 + x * -2) + x(6 + x)) = 33
((-12 + -2x) + x(6 + x)) = 33
(-12 + -2x + (6 * x + x * x)) = 33
(-12 + -2x + (6x + x2)) = 33

Combine like terms: -2x + 6x = 4x
(-12 + 4x + x2) = 33

Solving
-12 + 4x + x2 = 33

Solving for variable 'x'.

Reorder the terms:
-12 + -33 + 4x + x2 = 33 + -33

Combine like terms: -12 + -33 = -45
-45 + 4x + x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-45 + 4x + x2 = 0

Factor a trinomial.
(-9 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-9, 5}