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Simplifying 6(2 + -1x)(x + 7) = 0 Reorder the terms: 6(2 + -1x)(7 + x) = 0 Multiply (2 + -1x) * (7 + x) 6(2(7 + x) + -1x * (7 + x)) = 0 6((7 * 2 + x * 2) + -1x * (7 + x)) = 0 6((14 + 2x) + -1x * (7 + x)) = 0 6(14 + 2x + (7 * -1x + x * -1x)) = 0 6(14 + 2x + (-7x + -1x2)) = 0 Combine like terms: 2x + -7x = -5x 6(14 + -5x + -1x2) = 0 (14 * 6 + -5x * 6 + -1x2 * 6) = 0 (84 + -30x + -6x2) = 0 Solving 84 + -30x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(14 + -5x + -1x2) = 0 Factor a trinomial. 6((2 + -1x)(7 + x)) = 0 Ignore the factor 6.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 = 2Subproblem 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 = -7Solution
x = {2, -7}
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