(2x+6)(-7x+14)=0

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Solution for (2x+6)(-7x+14)=0 equation:


Simplifying
(2x + 6)(-7x + 14) = 0

Reorder the terms:
(6 + 2x)(-7x + 14) = 0

Reorder the terms:
(6 + 2x)(14 + -7x) = 0

Multiply (6 + 2x) * (14 + -7x)
(6(14 + -7x) + 2x * (14 + -7x)) = 0
((14 * 6 + -7x * 6) + 2x * (14 + -7x)) = 0
((84 + -42x) + 2x * (14 + -7x)) = 0
(84 + -42x + (14 * 2x + -7x * 2x)) = 0
(84 + -42x + (28x + -14x2)) = 0

Combine like terms: -42x + 28x = -14x
(84 + -14x + -14x2) = 0

Solving
84 + -14x + -14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14'.
14(6 + -1x + -1x2) = 0

Factor a trinomial.
14((2 + -1x)(3 + x)) = 0

Ignore the factor 14.

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {2, -3}

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