(3x+7)(-2x-13)=0

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Solution for (3x+7)(-2x-13)=0 equation:


Simplifying
(3x + 7)(-2x + -13) = 0

Reorder the terms:
(7 + 3x)(-2x + -13) = 0

Reorder the terms:
(7 + 3x)(-13 + -2x) = 0

Multiply (7 + 3x) * (-13 + -2x)
(7(-13 + -2x) + 3x * (-13 + -2x)) = 0
((-13 * 7 + -2x * 7) + 3x * (-13 + -2x)) = 0
((-91 + -14x) + 3x * (-13 + -2x)) = 0
(-91 + -14x + (-13 * 3x + -2x * 3x)) = 0
(-91 + -14x + (-39x + -6x2)) = 0

Combine like terms: -14x + -39x = -53x
(-91 + -53x + -6x2) = 0

Solving
-91 + -53x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(91 + 53x + 6x2) = 0

Factor a trinomial.
-1((13 + 2x)(7 + 3x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(13 + 2x)' equal to zero and attempt to solve: Simplifying 13 + 2x = 0 Solving 13 + 2x = 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 + 2x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 2x = 0 + -13 2x = 0 + -13 Combine like terms: 0 + -13 = -13 2x = -13 Divide each side by '2'. x = -6.5 Simplifying x = -6.5

Subproblem 2

Set the factor '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Divide each side by '3'. x = -2.333333333 Simplifying x = -2.333333333

Solution

x = {-6.5, -2.333333333}

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