12x(x+1)+3=5(2x+1)+2

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Solution for 12x(x+1)+3=5(2x+1)+2 equation: 


Simplifying
12x(x + 1) + 3 = 5(2x + 1) + 2

Reorder the terms:
12x(1 + x) + 3 = 5(2x + 1) + 2
(1 * 12x + x * 12x) + 3 = 5(2x + 1) + 2
(12x + 12x2) + 3 = 5(2x + 1) + 2

Reorder the terms:
3 + 12x + 12x2 = 5(2x + 1) + 2

Reorder the terms:
3 + 12x + 12x2 = 5(1 + 2x) + 2
3 + 12x + 12x2 = (1 * 5 + 2x * 5) + 2
3 + 12x + 12x2 = (5 + 10x) + 2

Reorder the terms:
3 + 12x + 12x2 = 5 + 2 + 10x

Combine like terms: 5 + 2 = 7
3 + 12x + 12x2 = 7 + 10x

Solving
3 + 12x + 12x2 = 7 + 10x

Solving for variable 'x'.

Reorder the terms:
3 + -7 + 12x + -10x + 12x2 = 7 + 10x + -7 + -10x

Combine like terms: 3 + -7 = -4
-4 + 12x + -10x + 12x2 = 7 + 10x + -7 + -10x

Combine like terms: 12x + -10x = 2x
-4 + 2x + 12x2 = 7 + 10x + -7 + -10x

Reorder the terms:
-4 + 2x + 12x2 = 7 + -7 + 10x + -10x

Combine like terms: 7 + -7 = 0
-4 + 2x + 12x2 = 0 + 10x + -10x
-4 + 2x + 12x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-4 + 2x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + x + 6x2) = 0

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

Ignore the factor 2.

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

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-0.6666666667, 0.5}

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