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Simplifying x(8x + 7) = 3x2 + -16x + 42 Reorder the terms: x(7 + 8x) = 3x2 + -16x + 42 (7 * x + 8x * x) = 3x2 + -16x + 42 (7x + 8x2) = 3x2 + -16x + 42 Reorder the terms: 7x + 8x2 = 42 + -16x + 3x2 Solving 7x + 8x2 = 42 + -16x + 3x2 Solving for variable 'x'. Reorder the terms: -42 + 7x + 16x + 8x2 + -3x2 = 42 + -16x + 3x2 + -42 + 16x + -3x2 Combine like terms: 7x + 16x = 23x -42 + 23x + 8x2 + -3x2 = 42 + -16x + 3x2 + -42 + 16x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 -42 + 23x + 5x2 = 42 + -16x + 3x2 + -42 + 16x + -3x2 Reorder the terms: -42 + 23x + 5x2 = 42 + -42 + -16x + 16x + 3x2 + -3x2 Combine like terms: 42 + -42 = 0 -42 + 23x + 5x2 = 0 + -16x + 16x + 3x2 + -3x2 -42 + 23x + 5x2 = -16x + 16x + 3x2 + -3x2 Combine like terms: -16x + 16x = 0 -42 + 23x + 5x2 = 0 + 3x2 + -3x2 -42 + 23x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -42 + 23x + 5x2 = 0 Factor a trinomial. (-6 + -1x)(7 + -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 '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 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 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4Solution
x = {-6, 1.4}
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