(3x-2)(4x+7)=-14

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Solution for (3x-2)(4x+7)=-14 equation: 


Simplifying
(3x + -2)(4x + 7) = -14

Reorder the terms:
(-2 + 3x)(4x + 7) = -14

Reorder the terms:
(-2 + 3x)(7 + 4x) = -14

Multiply (-2 + 3x) * (7 + 4x)
(-2(7 + 4x) + 3x * (7 + 4x)) = -14
((7 * -2 + 4x * -2) + 3x * (7 + 4x)) = -14
((-14 + -8x) + 3x * (7 + 4x)) = -14
(-14 + -8x + (7 * 3x + 4x * 3x)) = -14
(-14 + -8x + (21x + 12x2)) = -14

Combine like terms: -8x + 21x = 13x
(-14 + 13x + 12x2) = -14

Add '14' to each side of the equation.
-14 + 13x + 14 + 12x2 = -14 + 14

Reorder the terms:
-14 + 14 + 13x + 12x2 = -14 + 14

Combine like terms: -14 + 14 = 0
0 + 13x + 12x2 = -14 + 14
13x + 12x2 = -14 + 14

Combine like terms: -14 + 14 = 0
13x + 12x2 = 0

Solving
13x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(13 + 12x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(13 + 12x)' equal to zero and attempt to solve:

Simplifying
13 + 12x = 0

Solving
13 + 12x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 12x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 12x = 0 + -13
12x = 0 + -13

Combine like terms: 0 + -13 = -13
12x = -13

Divide each side by '12'.
x = -1.083333333

Simplifying
x = -1.083333333
Solution
x = {0, -1.083333333}

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