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Simplifying (4x + 9)(x + -4) = 16x + 36 Reorder the terms: (9 + 4x)(x + -4) = 16x + 36 Reorder the terms: (9 + 4x)(-4 + x) = 16x + 36 Multiply (9 + 4x) * (-4 + x) (9(-4 + x) + 4x * (-4 + x)) = 16x + 36 ((-4 * 9 + x * 9) + 4x * (-4 + x)) = 16x + 36 ((-36 + 9x) + 4x * (-4 + x)) = 16x + 36 (-36 + 9x + (-4 * 4x + x * 4x)) = 16x + 36 (-36 + 9x + (-16x + 4x2)) = 16x + 36 Combine like terms: 9x + -16x = -7x (-36 + -7x + 4x2) = 16x + 36 Reorder the terms: -36 + -7x + 4x2 = 36 + 16x Solving -36 + -7x + 4x2 = 36 + 16x Solving for variable 'x'. Reorder the terms: -36 + -36 + -7x + -16x + 4x2 = 36 + 16x + -36 + -16x Combine like terms: -36 + -36 = -72 -72 + -7x + -16x + 4x2 = 36 + 16x + -36 + -16x Combine like terms: -7x + -16x = -23x -72 + -23x + 4x2 = 36 + 16x + -36 + -16x Reorder the terms: -72 + -23x + 4x2 = 36 + -36 + 16x + -16x Combine like terms: 36 + -36 = 0 -72 + -23x + 4x2 = 0 + 16x + -16x -72 + -23x + 4x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -72 + -23x + 4x2 = 0 Factor a trinomial. (-9 + -4x)(8 + -1x) = 0Subproblem 1
Set the factor '(-9 + -4x)' equal to zero and attempt to solve: Simplifying -9 + -4x = 0 Solving -9 + -4x = 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 + -4x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4x = 0 + 9 -4x = 0 + 9 Combine like terms: 0 + 9 = 9 -4x = 9 Divide each side by '-4'. x = -2.25 Simplifying x = -2.25Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 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 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-2.25, 8}
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