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Simplifying x(8x + 4) = 3x2 + -2x + 27 Reorder the terms: x(4 + 8x) = 3x2 + -2x + 27 (4 * x + 8x * x) = 3x2 + -2x + 27 (4x + 8x2) = 3x2 + -2x + 27 Reorder the terms: 4x + 8x2 = 27 + -2x + 3x2 Solving 4x + 8x2 = 27 + -2x + 3x2 Solving for variable 'x'. Reorder the terms: -27 + 4x + 2x + 8x2 + -3x2 = 27 + -2x + 3x2 + -27 + 2x + -3x2 Combine like terms: 4x + 2x = 6x -27 + 6x + 8x2 + -3x2 = 27 + -2x + 3x2 + -27 + 2x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 -27 + 6x + 5x2 = 27 + -2x + 3x2 + -27 + 2x + -3x2 Reorder the terms: -27 + 6x + 5x2 = 27 + -27 + -2x + 2x + 3x2 + -3x2 Combine like terms: 27 + -27 = 0 -27 + 6x + 5x2 = 0 + -2x + 2x + 3x2 + -3x2 -27 + 6x + 5x2 = -2x + 2x + 3x2 + -3x2 Combine like terms: -2x + 2x = 0 -27 + 6x + 5x2 = 0 + 3x2 + -3x2 -27 + 6x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -27 + 6x + 5x2 = 0 Factor a trinomial. (-3 + -1x)(9 + -5x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(9 + -5x)' equal to zero and attempt to solve: Simplifying 9 + -5x = 0 Solving 9 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5x = 0 + -9 -5x = 0 + -9 Combine like terms: 0 + -9 = -9 -5x = -9 Divide each side by '-5'. x = 1.8 Simplifying x = 1.8Solution
x = {-3, 1.8}
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