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Simplifying 12x2 = 16x + 28 Reorder the terms: 12x2 = 28 + 16x Solving 12x2 = 28 + 16x Solving for variable 'x'. Reorder the terms: -28 + -16x + 12x2 = 28 + 16x + -28 + -16x Reorder the terms: -28 + -16x + 12x2 = 28 + -28 + 16x + -16x Combine like terms: 28 + -28 = 0 -28 + -16x + 12x2 = 0 + 16x + -16x -28 + -16x + 12x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -28 + -16x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + -4x + 3x2) = 0 Factor a trinomial. 4((-1 + -1x)(7 + -3x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 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 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333Solution
x = {-1, 2.333333333}
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