(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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