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Simplifying (3x + 4)(x + -5) = 9x + 12 Reorder the terms: (4 + 3x)(x + -5) = 9x + 12 Reorder the terms: (4 + 3x)(-5 + x) = 9x + 12 Multiply (4 + 3x) * (-5 + x) (4(-5 + x) + 3x * (-5 + x)) = 9x + 12 ((-5 * 4 + x * 4) + 3x * (-5 + x)) = 9x + 12 ((-20 + 4x) + 3x * (-5 + x)) = 9x + 12 (-20 + 4x + (-5 * 3x + x * 3x)) = 9x + 12 (-20 + 4x + (-15x + 3x2)) = 9x + 12 Combine like terms: 4x + -15x = -11x (-20 + -11x + 3x2) = 9x + 12 Reorder the terms: -20 + -11x + 3x2 = 12 + 9x Solving -20 + -11x + 3x2 = 12 + 9x Solving for variable 'x'. Reorder the terms: -20 + -12 + -11x + -9x + 3x2 = 12 + 9x + -12 + -9x Combine like terms: -20 + -12 = -32 -32 + -11x + -9x + 3x2 = 12 + 9x + -12 + -9x Combine like terms: -11x + -9x = -20x -32 + -20x + 3x2 = 12 + 9x + -12 + -9x Reorder the terms: -32 + -20x + 3x2 = 12 + -12 + 9x + -9x Combine like terms: 12 + -12 = 0 -32 + -20x + 3x2 = 0 + 9x + -9x -32 + -20x + 3x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -32 + -20x + 3x2 = 0 Factor a trinomial. (-4 + -3x)(8 + -1x) = 0Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 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 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333Subproblem 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 = {-1.333333333, 8}
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