(3x-7)(x+2)=-12

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Solution for (3x-7)(x+2)=-12 equation: 


Simplifying
(3x + -7)(x + 2) = -12

Reorder the terms:
(-7 + 3x)(x + 2) = -12

Reorder the terms:
(-7 + 3x)(2 + x) = -12

Multiply (-7 + 3x) * (2 + x)
(-7(2 + x) + 3x * (2 + x)) = -12
((2 * -7 + x * -7) + 3x * (2 + x)) = -12
((-14 + -7x) + 3x * (2 + x)) = -12
(-14 + -7x + (2 * 3x + x * 3x)) = -12
(-14 + -7x + (6x + 3x2)) = -12

Combine like terms: -7x + 6x = -1x
(-14 + -1x + 3x2) = -12

Solving
-14 + -1x + 3x2 = -12

Solving for variable 'x'.

Reorder the terms:
-14 + 12 + -1x + 3x2 = -12 + 12

Combine like terms: -14 + 12 = -2
-2 + -1x + 3x2 = -12 + 12

Combine like terms: -12 + 12 = 0
-2 + -1x + 3x2 = 0

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


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 + -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 = {-0.6666666667, 1}

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