(x-5)(x+3)=33

Solution for (x-5)(x+3)=33 equation:

Simplifying
(x + -5)(x + 3) = 33

Reorder the terms:
(-5 + x)(x + 3) = 33

Reorder the terms:
(-5 + x)(3 + x) = 33

Multiply (-5 + x) * (3 + x)
(-5(3 + x) + x(3 + x)) = 33
((3 * -5 + x * -5) + x(3 + x)) = 33
((-15 + -5x) + x(3 + x)) = 33
(-15 + -5x + (3 * x + x * x)) = 33
(-15 + -5x + (3x + x2)) = 33

Combine like terms: -5x + 3x = -2x
(-15 + -2x + x2) = 33

Solving
-15 + -2x + x2 = 33

Solving for variable 'x'.

Reorder the terms:
-15 + -33 + -2x + x2 = 33 + -33

Combine like terms: -15 + -33 = -48
-48 + -2x + x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-48 + -2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

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

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

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 8}