(x-9)(x+3)=28

Solution for (x-9)(x+3)=28 equation:

Simplifying
(x + -9)(x + 3) = 28

Reorder the terms:
(-9 + x)(x + 3) = 28

Reorder the terms:
(-9 + x)(3 + x) = 28

Multiply (-9 + x) * (3 + x)
(-9(3 + x) + x(3 + x)) = 28
((3 * -9 + x * -9) + x(3 + x)) = 28
((-27 + -9x) + x(3 + x)) = 28
(-27 + -9x + (3 * x + x * x)) = 28
(-27 + -9x + (3x + x2)) = 28

Combine like terms: -9x + 3x = -6x
(-27 + -6x + x2) = 28

Solving
-27 + -6x + x2 = 28

Solving for variable 'x'.

Reorder the terms:
-27 + -28 + -6x + x2 = 28 + -28

Combine like terms: -27 + -28 = -55
-55 + -6x + x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-55 + -6x + x2 = 0

Factor a trinomial.
(-5 + -1x)(11 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-5, 11}