12x(x+3)=4(2x+9)+4x

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Solution for 12x(x+3)=4(2x+9)+4x equation: 


Simplifying
12x(x + 3) = 4(2x + 9) + 4x

Reorder the terms:
12x(3 + x) = 4(2x + 9) + 4x
(3 * 12x + x * 12x) = 4(2x + 9) + 4x
(36x + 12x2) = 4(2x + 9) + 4x

Reorder the terms:
36x + 12x2 = 4(9 + 2x) + 4x
36x + 12x2 = (9 * 4 + 2x * 4) + 4x
36x + 12x2 = (36 + 8x) + 4x

Combine like terms: 8x + 4x = 12x
36x + 12x2 = 36 + 12x

Solving
36x + 12x2 = 36 + 12x

Solving for variable 'x'.

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

Combine like terms: 36x + -12x = 24x
-36 + 24x + 12x2 = 36 + 12x + -36 + -12x

Reorder the terms:
-36 + 24x + 12x2 = 36 + -36 + 12x + -12x

Combine like terms: 36 + -36 = 0
-36 + 24x + 12x2 = 0 + 12x + -12x
-36 + 24x + 12x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-36 + 24x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-3 + 2x + x2) = 0

Factor a trinomial.
12((-3 + -1x)(1 + -1x)) = 0

Ignore the factor 12.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-3, 1}

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