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Simplifying (7x + 7)(x + -5) = 0 Reorder the terms: (7 + 7x)(x + -5) = 0 Reorder the terms: (7 + 7x)(-5 + x) = 0 Multiply (7 + 7x) * (-5 + x) (7(-5 + x) + 7x * (-5 + x)) = 0 ((-5 * 7 + x * 7) + 7x * (-5 + x)) = 0 ((-35 + 7x) + 7x * (-5 + x)) = 0 (-35 + 7x + (-5 * 7x + x * 7x)) = 0 (-35 + 7x + (-35x + 7x2)) = 0 Combine like terms: 7x + -35x = -28x (-35 + -28x + 7x2) = 0 Solving -35 + -28x + 7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(-5 + -4x + x2) = 0 Factor a trinomial. 7((-1 + -1x)(5 + -1x)) = 0 Ignore the factor 7.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 = -1Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-1, 5}
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