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

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


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

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

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

Multiply (-4 + 3x) * (3 + x)
(-4(3 + x) + 3x * (3 + x)) = -14
((3 * -4 + x * -4) + 3x * (3 + x)) = -14
((-12 + -4x) + 3x * (3 + x)) = -14
(-12 + -4x + (3 * 3x + x * 3x)) = -14
(-12 + -4x + (9x + 3x2)) = -14

Combine like terms: -4x + 9x = 5x
(-12 + 5x + 3x2) = -14

Solving
-12 + 5x + 3x2 = -14

Solving for variable 'x'.

Reorder the terms:
-12 + 14 + 5x + 3x2 = -14 + 14

Combine like terms: -12 + 14 = 2
2 + 5x + 3x2 = -14 + 14

Combine like terms: -14 + 14 = 0
2 + 5x + 3x2 = 0

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


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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1

Subproblem 2
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
Solution
x = {-1, -0.6666666667}

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