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Simplifying x(5x + 5) = 2x2 + -9x + 24 Reorder the terms: x(5 + 5x) = 2x2 + -9x + 24 (5 * x + 5x * x) = 2x2 + -9x + 24 (5x + 5x2) = 2x2 + -9x + 24 Reorder the terms: 5x + 5x2 = 24 + -9x + 2x2 Solving 5x + 5x2 = 24 + -9x + 2x2 Solving for variable 'x'. Reorder the terms: -24 + 5x + 9x + 5x2 + -2x2 = 24 + -9x + 2x2 + -24 + 9x + -2x2 Combine like terms: 5x + 9x = 14x -24 + 14x + 5x2 + -2x2 = 24 + -9x + 2x2 + -24 + 9x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -24 + 14x + 3x2 = 24 + -9x + 2x2 + -24 + 9x + -2x2 Reorder the terms: -24 + 14x + 3x2 = 24 + -24 + -9x + 9x + 2x2 + -2x2 Combine like terms: 24 + -24 = 0 -24 + 14x + 3x2 = 0 + -9x + 9x + 2x2 + -2x2 -24 + 14x + 3x2 = -9x + 9x + 2x2 + -2x2 Combine like terms: -9x + 9x = 0 -24 + 14x + 3x2 = 0 + 2x2 + -2x2 -24 + 14x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -24 + 14x + 3x2 = 0 Factor a trinomial. (-6 + -1x)(4 + -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 '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {-6, 1.333333333}
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