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Simplifying (2x + 9)(x + -6) = 4x + 18 Reorder the terms: (9 + 2x)(x + -6) = 4x + 18 Reorder the terms: (9 + 2x)(-6 + x) = 4x + 18 Multiply (9 + 2x) * (-6 + x) (9(-6 + x) + 2x * (-6 + x)) = 4x + 18 ((-6 * 9 + x * 9) + 2x * (-6 + x)) = 4x + 18 ((-54 + 9x) + 2x * (-6 + x)) = 4x + 18 (-54 + 9x + (-6 * 2x + x * 2x)) = 4x + 18 (-54 + 9x + (-12x + 2x2)) = 4x + 18 Combine like terms: 9x + -12x = -3x (-54 + -3x + 2x2) = 4x + 18 Reorder the terms: -54 + -3x + 2x2 = 18 + 4x Solving -54 + -3x + 2x2 = 18 + 4x Solving for variable 'x'. Reorder the terms: -54 + -18 + -3x + -4x + 2x2 = 18 + 4x + -18 + -4x Combine like terms: -54 + -18 = -72 -72 + -3x + -4x + 2x2 = 18 + 4x + -18 + -4x Combine like terms: -3x + -4x = -7x -72 + -7x + 2x2 = 18 + 4x + -18 + -4x Reorder the terms: -72 + -7x + 2x2 = 18 + -18 + 4x + -4x Combine like terms: 18 + -18 = 0 -72 + -7x + 2x2 = 0 + 4x + -4x -72 + -7x + 2x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -72 + -7x + 2x2 = 0 Factor a trinomial. (-9 + -2x)(8 + -1x) = 0Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 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 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5Subproblem 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 = {-4.5, 8}
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