3x(x+4)=36

Solution for 3x(x+4)=36 equation:

Simplifying
3x(x + 4) = 36

Reorder the terms:
3x(4 + x) = 36
(4 * 3x + x * 3x) = 36
(12x + 3x2) = 36

Solving
12x + 3x2 = 36

Solving for variable 'x'.

Reorder the terms:
-36 + 12x + 3x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 4x + x2) = 0

Factor a trinomial.
3((-6 + -1x)(2 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-6, 2}