4x(3x+1)+12(3x+1)=

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Solution for 4x(3x+1)+12(3x+1)= equation: 


Simplifying
4x(3x + 1) + 12(3x + 1) = 0

Reorder the terms:
4x(1 + 3x) + 12(3x + 1) = 0
(1 * 4x + 3x * 4x) + 12(3x + 1) = 0
(4x + 12x2) + 12(3x + 1) = 0

Reorder the terms:
4x + 12x2 + 12(1 + 3x) = 0
4x + 12x2 + (1 * 12 + 3x * 12) = 0
4x + 12x2 + (12 + 36x) = 0

Reorder the terms:
12 + 4x + 36x + 12x2 = 0

Combine like terms: 4x + 36x = 40x
12 + 40x + 12x2 = 0

Solving
12 + 40x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 10x + 3x2) = 0

Factor a trinomial.
4((3 + x)(1 + 3x)) = 0

Ignore the factor 4.

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3

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

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-3, -0.3333333333}

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