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Simplifying (6 + -1x)(14 + 2x) = 84 Multiply (6 + -1x) * (14 + 2x) (6(14 + 2x) + -1x * (14 + 2x)) = 84 ((14 * 6 + 2x * 6) + -1x * (14 + 2x)) = 84 ((84 + 12x) + -1x * (14 + 2x)) = 84 (84 + 12x + (14 * -1x + 2x * -1x)) = 84 (84 + 12x + (-14x + -2x2)) = 84 Combine like terms: 12x + -14x = -2x (84 + -2x + -2x2) = 84 Add '-84' to each side of the equation. 84 + -2x + -84 + -2x2 = 84 + -84 Reorder the terms: 84 + -84 + -2x + -2x2 = 84 + -84 Combine like terms: 84 + -84 = 0 0 + -2x + -2x2 = 84 + -84 -2x + -2x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -2x + -2x2 = 0 Solving -2x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2x'. -2x(1 + x) = 0 Ignore the factor -2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {0, -1}
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