3x(x+4)-4=2(x+4)+x

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


Simplifying
3x(x + 4) + -4 = 2(x + 4) + x

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

Reorder the terms:
-4 + 12x + 3x2 = 2(x + 4) + x

Reorder the terms:
-4 + 12x + 3x2 = 2(4 + x) + x
-4 + 12x + 3x2 = (4 * 2 + x * 2) + x
-4 + 12x + 3x2 = (8 + 2x) + x

Combine like terms: 2x + x = 3x
-4 + 12x + 3x2 = 8 + 3x

Solving
-4 + 12x + 3x2 = 8 + 3x

Solving for variable 'x'.

Reorder the terms:
-4 + -8 + 12x + -3x + 3x2 = 8 + 3x + -8 + -3x

Combine like terms: -4 + -8 = -12
-12 + 12x + -3x + 3x2 = 8 + 3x + -8 + -3x

Combine like terms: 12x + -3x = 9x
-12 + 9x + 3x2 = 8 + 3x + -8 + -3x

Reorder the terms:
-12 + 9x + 3x2 = 8 + -8 + 3x + -3x

Combine like terms: 8 + -8 = 0
-12 + 9x + 3x2 = 0 + 3x + -3x
-12 + 9x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-12 + 9x + 3x2 = 0

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

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 1}

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