(x-3)(x+18)=12x

Solution for (x-3)(x+18)=12x equation:

Simplifying
(x + -3)(x + 18) = 12x

Reorder the terms:
(-3 + x)(x + 18) = 12x

Reorder the terms:
(-3 + x)(18 + x) = 12x

Multiply (-3 + x) * (18 + x)
(-3(18 + x) + x(18 + x)) = 12x
((18 * -3 + x * -3) + x(18 + x)) = 12x
((-54 + -3x) + x(18 + x)) = 12x
(-54 + -3x + (18 * x + x * x)) = 12x
(-54 + -3x + (18x + x2)) = 12x

Combine like terms: -3x + 18x = 15x
(-54 + 15x + x2) = 12x

Solving
-54 + 15x + x2 = 12x

Solving for variable 'x'.

Reorder the terms:
-54 + 15x + -12x + x2 = 12x + -12x

Combine like terms: 15x + -12x = 3x
-54 + 3x + x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-54 + 3x + x2 = 0

Factor a trinomial.
(-9 + -1x)(6 + -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 '(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 = {-9, 6}