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Simplifying 3x2 = 45x + -78 Reorder the terms: 3x2 = -78 + 45x Solving 3x2 = -78 + 45x Solving for variable 'x'. Reorder the terms: 78 + -45x + 3x2 = -78 + 45x + 78 + -45x Reorder the terms: 78 + -45x + 3x2 = -78 + 78 + 45x + -45x Combine like terms: -78 + 78 = 0 78 + -45x + 3x2 = 0 + 45x + -45x 78 + -45x + 3x2 = 45x + -45x Combine like terms: 45x + -45x = 0 78 + -45x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(26 + -15x + x2) = 0 Factor a trinomial. 3((2 + -1x)(13 + -1x)) = 0 Ignore the factor 3.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 '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Solution
x = {2, 13}
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