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Simplifying 12x2 = 69x + -45 Reorder the terms: 12x2 = -45 + 69x Solving 12x2 = -45 + 69x Solving for variable 'x'. Reorder the terms: 45 + -69x + 12x2 = -45 + 69x + 45 + -69x Reorder the terms: 45 + -69x + 12x2 = -45 + 45 + 69x + -69x Combine like terms: -45 + 45 = 0 45 + -69x + 12x2 = 0 + 69x + -69x 45 + -69x + 12x2 = 69x + -69x Combine like terms: 69x + -69x = 0 45 + -69x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(15 + -23x + 4x2) = 0 Factor a trinomial. 3((3 + -4x)(5 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Subproblem 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 = {0.75, 5}
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