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Simplifying x(5x + 13) = 2x2 + -3x + 12 Reorder the terms: x(13 + 5x) = 2x2 + -3x + 12 (13 * x + 5x * x) = 2x2 + -3x + 12 (13x + 5x2) = 2x2 + -3x + 12 Reorder the terms: 13x + 5x2 = 12 + -3x + 2x2 Solving 13x + 5x2 = 12 + -3x + 2x2 Solving for variable 'x'. Reorder the terms: -12 + 13x + 3x + 5x2 + -2x2 = 12 + -3x + 2x2 + -12 + 3x + -2x2 Combine like terms: 13x + 3x = 16x -12 + 16x + 5x2 + -2x2 = 12 + -3x + 2x2 + -12 + 3x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -12 + 16x + 3x2 = 12 + -3x + 2x2 + -12 + 3x + -2x2 Reorder the terms: -12 + 16x + 3x2 = 12 + -12 + -3x + 3x + 2x2 + -2x2 Combine like terms: 12 + -12 = 0 -12 + 16x + 3x2 = 0 + -3x + 3x + 2x2 + -2x2 -12 + 16x + 3x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 -12 + 16x + 3x2 = 0 + 2x2 + -2x2 -12 + 16x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12 + 16x + 3x2 = 0 Factor a trinomial. (-6 + -1x)(2 + -3x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-6, 0.6666666667}
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