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Simplifying x(9x + 3) = 4x2 + -24x + 56 Reorder the terms: x(3 + 9x) = 4x2 + -24x + 56 (3 * x + 9x * x) = 4x2 + -24x + 56 (3x + 9x2) = 4x2 + -24x + 56 Reorder the terms: 3x + 9x2 = 56 + -24x + 4x2 Solving 3x + 9x2 = 56 + -24x + 4x2 Solving for variable 'x'. Reorder the terms: -56 + 3x + 24x + 9x2 + -4x2 = 56 + -24x + 4x2 + -56 + 24x + -4x2 Combine like terms: 3x + 24x = 27x -56 + 27x + 9x2 + -4x2 = 56 + -24x + 4x2 + -56 + 24x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 -56 + 27x + 5x2 = 56 + -24x + 4x2 + -56 + 24x + -4x2 Reorder the terms: -56 + 27x + 5x2 = 56 + -56 + -24x + 24x + 4x2 + -4x2 Combine like terms: 56 + -56 = 0 -56 + 27x + 5x2 = 0 + -24x + 24x + 4x2 + -4x2 -56 + 27x + 5x2 = -24x + 24x + 4x2 + -4x2 Combine like terms: -24x + 24x = 0 -56 + 27x + 5x2 = 0 + 4x2 + -4x2 -56 + 27x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -56 + 27x + 5x2 = 0 Factor a trinomial. (-7 + -1x)(8 + -5x) = 0Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 2
Set the factor '(8 + -5x)' equal to zero and attempt to solve: Simplifying 8 + -5x = 0 Solving 8 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x = 0 + -8 -5x = 0 + -8 Combine like terms: 0 + -8 = -8 -5x = -8 Divide each side by '-5'. x = 1.6 Simplifying x = 1.6Solution
x = {-7, 1.6}
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