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Simplifying x(9x + 15) = 4x2 + -16x + 28 Reorder the terms: x(15 + 9x) = 4x2 + -16x + 28 (15 * x + 9x * x) = 4x2 + -16x + 28 (15x + 9x2) = 4x2 + -16x + 28 Reorder the terms: 15x + 9x2 = 28 + -16x + 4x2 Solving 15x + 9x2 = 28 + -16x + 4x2 Solving for variable 'x'. Reorder the terms: -28 + 15x + 16x + 9x2 + -4x2 = 28 + -16x + 4x2 + -28 + 16x + -4x2 Combine like terms: 15x + 16x = 31x -28 + 31x + 9x2 + -4x2 = 28 + -16x + 4x2 + -28 + 16x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 -28 + 31x + 5x2 = 28 + -16x + 4x2 + -28 + 16x + -4x2 Reorder the terms: -28 + 31x + 5x2 = 28 + -28 + -16x + 16x + 4x2 + -4x2 Combine like terms: 28 + -28 = 0 -28 + 31x + 5x2 = 0 + -16x + 16x + 4x2 + -4x2 -28 + 31x + 5x2 = -16x + 16x + 4x2 + -4x2 Combine like terms: -16x + 16x = 0 -28 + 31x + 5x2 = 0 + 4x2 + -4x2 -28 + 31x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -28 + 31x + 5x2 = 0 Factor a trinomial. (-7 + -1x)(4 + -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 '(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 = {-7, 0.8}
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