(x-3)(x+9)=-27

Solution for (x-3)(x+9)=-27 equation:

Simplifying
(x + -3)(x + 9) = -27

Reorder the terms:
(-3 + x)(x + 9) = -27

Reorder the terms:
(-3 + x)(9 + x) = -27

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

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

Add '27' to each side of the equation.
-27 + 6x + 27 + x2 = -27 + 27

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

Combine like terms: -27 + 27 = 0
0 + 6x + x2 = -27 + 27
6x + x2 = -27 + 27

Combine like terms: -27 + 27 = 0
6x + x2 = 0

Solving
6x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {0, -6}