(2x-6)(x+7)=0

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Solution for (2x-6)(x+7)=0 equation:


Simplifying
(2x + -6)(x + 7) = 0

Reorder the terms:
(-6 + 2x)(x + 7) = 0

Reorder the terms:
(-6 + 2x)(7 + x) = 0

Multiply (-6 + 2x) * (7 + x)
(-6(7 + x) + 2x * (7 + x)) = 0
((7 * -6 + x * -6) + 2x * (7 + x)) = 0
((-42 + -6x) + 2x * (7 + x)) = 0
(-42 + -6x + (7 * 2x + x * 2x)) = 0
(-42 + -6x + (14x + 2x2)) = 0

Combine like terms: -6x + 14x = 8x
(-42 + 8x + 2x2) = 0

Solving
-42 + 8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 4x + x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-7, 3}

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