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

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


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

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

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

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

Combine like terms: -14x + 2x = -12x
(14 + -12x + -2x2) = 0

Solving
14 + -12x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -6x + -1x2) = 0

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

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

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

Solution

x = {1, -7}

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