(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.
(-8 + -1x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-8, 6}