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Simplifying 0 = 45 + 6x + -3x2 Solving 0 = 45 + 6x + -3x2 Solving for variable 'x'. Combine like terms: 0 + -45 = -45 -45 + -6x + 3x2 = 45 + 6x + -3x2 + -45 + -6x + 3x2 Reorder the terms: -45 + -6x + 3x2 = 45 + -45 + 6x + -6x + -3x2 + 3x2 Combine like terms: 45 + -45 = 0 -45 + -6x + 3x2 = 0 + 6x + -6x + -3x2 + 3x2 -45 + -6x + 3x2 = 6x + -6x + -3x2 + 3x2 Combine like terms: 6x + -6x = 0 -45 + -6x + 3x2 = 0 + -3x2 + 3x2 -45 + -6x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -45 + -6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + -2x + x2) = 0 Factor a trinomial. 3((-3 + -1x)(5 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 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 = {-3, 5}
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