4x(x+3)=216

Solution for 4x(x+3)=216 equation:

Simplifying
4x(x + 3) = 216

Reorder the terms:
4x(3 + x) = 216
(3 * 4x + x * 4x) = 216
(12x + 4x2) = 216

Solving
12x + 4x2 = 216

Solving for variable 'x'.

Reorder the terms:
-216 + 12x + 4x2 = 216 + -216

Combine like terms: 216 + -216 = 0
-216 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-54 + 3x + x2) = 0

Factor a trinomial.
4((-9 + -1x)(6 + -1x)) = 0

Ignore the factor 4.
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}