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Simplifying 0 = 6x2 + 30x + -84 Reorder the terms: 0 = -84 + 30x + 6x2 Solving 0 = -84 + 30x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 84 = 84 84 + -30x + -6x2 = -84 + 30x + 6x2 + 84 + -30x + -6x2 Reorder the terms: 84 + -30x + -6x2 = -84 + 84 + 30x + -30x + 6x2 + -6x2 Combine like terms: -84 + 84 = 0 84 + -30x + -6x2 = 0 + 30x + -30x + 6x2 + -6x2 84 + -30x + -6x2 = 30x + -30x + 6x2 + -6x2 Combine like terms: 30x + -30x = 0 84 + -30x + -6x2 = 0 + 6x2 + -6x2 84 + -30x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 84 + -30x + -6x2 = 0 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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