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Simplifying x(8x + 20) = 3x2 + -6x + 24 Reorder the terms: x(20 + 8x) = 3x2 + -6x + 24 (20 * x + 8x * x) = 3x2 + -6x + 24 (20x + 8x2) = 3x2 + -6x + 24 Reorder the terms: 20x + 8x2 = 24 + -6x + 3x2 Solving 20x + 8x2 = 24 + -6x + 3x2 Solving for variable 'x'. Reorder the terms: -24 + 20x + 6x + 8x2 + -3x2 = 24 + -6x + 3x2 + -24 + 6x + -3x2 Combine like terms: 20x + 6x = 26x -24 + 26x + 8x2 + -3x2 = 24 + -6x + 3x2 + -24 + 6x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 -24 + 26x + 5x2 = 24 + -6x + 3x2 + -24 + 6x + -3x2 Reorder the terms: -24 + 26x + 5x2 = 24 + -24 + -6x + 6x + 3x2 + -3x2 Combine like terms: 24 + -24 = 0 -24 + 26x + 5x2 = 0 + -6x + 6x + 3x2 + -3x2 -24 + 26x + 5x2 = -6x + 6x + 3x2 + -3x2 Combine like terms: -6x + 6x = 0 -24 + 26x + 5x2 = 0 + 3x2 + -3x2 -24 + 26x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -24 + 26x + 5x2 = 0 Factor a trinomial. (-6 + -1x)(4 + -5x) = 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 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 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 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8Solution
x = {-6, 0.8}
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