(-7x-3)(6x+7)+28x+12=0

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Solution for (-7x-3)(6x+7)+28x+12=0 equation: 


Simplifying
(-7x + -3)(6x + 7) + 28x + 12 = 0

Reorder the terms:
(-3 + -7x)(6x + 7) + 28x + 12 = 0

Reorder the terms:
(-3 + -7x)(7 + 6x) + 28x + 12 = 0

Multiply (-3 + -7x) * (7 + 6x)
(-3(7 + 6x) + -7x * (7 + 6x)) + 28x + 12 = 0
((7 * -3 + 6x * -3) + -7x * (7 + 6x)) + 28x + 12 = 0
((-21 + -18x) + -7x * (7 + 6x)) + 28x + 12 = 0
(-21 + -18x + (7 * -7x + 6x * -7x)) + 28x + 12 = 0
(-21 + -18x + (-49x + -42x2)) + 28x + 12 = 0

Combine like terms: -18x + -49x = -67x
(-21 + -67x + -42x2) + 28x + 12 = 0

Reorder the terms:
-21 + 12 + -67x + 28x + -42x2 = 0

Combine like terms: -21 + 12 = -9
-9 + -67x + 28x + -42x2 = 0

Combine like terms: -67x + 28x = -39x
-9 + -39x + -42x2 = 0

Solving
-9 + -39x + -42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(3 + 13x + 14x2) = 0

Factor a trinomial.
-3((1 + 2x)(3 + 7x)) = 0

Ignore the factor -3.

Subproblem 1
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

Subproblem 2
Set the factor '(3 + 7x)' equal to zero and attempt to solve:

Simplifying
3 + 7x = 0

Solving
3 + 7x = 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 + 7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7x = 0 + -3
7x = 0 + -3

Combine like terms: 0 + -3 = -3
7x = -3

Divide each side by '7'.
x = -0.4285714286

Simplifying
x = -0.4285714286
Solution
x = {-0.5, -0.4285714286}

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