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Simplifying (-7x + 7)(x + 6) = 0 Reorder the terms: (7 + -7x)(x + 6) = 0 Reorder the terms: (7 + -7x)(6 + x) = 0 Multiply (7 + -7x) * (6 + x) (7(6 + x) + -7x * (6 + x)) = 0 ((6 * 7 + x * 7) + -7x * (6 + x)) = 0 ((42 + 7x) + -7x * (6 + x)) = 0 (42 + 7x + (6 * -7x + x * -7x)) = 0 (42 + 7x + (-42x + -7x2)) = 0 Combine like terms: 7x + -42x = -35x (42 + -35x + -7x2) = 0 Solving 42 + -35x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(6 + -5x + -1x2) = 0 Factor a trinomial. 7((1 + -1x)(6 + x)) = 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {1, -6}
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