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Simplifying (3x + 8)(4x + -1) = -3(x + -9) Reorder the terms: (8 + 3x)(4x + -1) = -3(x + -9) Reorder the terms: (8 + 3x)(-1 + 4x) = -3(x + -9) Multiply (8 + 3x) * (-1 + 4x) (8(-1 + 4x) + 3x * (-1 + 4x)) = -3(x + -9) ((-1 * 8 + 4x * 8) + 3x * (-1 + 4x)) = -3(x + -9) ((-8 + 32x) + 3x * (-1 + 4x)) = -3(x + -9) (-8 + 32x + (-1 * 3x + 4x * 3x)) = -3(x + -9) (-8 + 32x + (-3x + 12x2)) = -3(x + -9) Combine like terms: 32x + -3x = 29x (-8 + 29x + 12x2) = -3(x + -9) Reorder the terms: -8 + 29x + 12x2 = -3(-9 + x) -8 + 29x + 12x2 = (-9 * -3 + x * -3) -8 + 29x + 12x2 = (27 + -3x) Solving -8 + 29x + 12x2 = 27 + -3x Solving for variable 'x'. Reorder the terms: -8 + -27 + 29x + 3x + 12x2 = 27 + -3x + -27 + 3x Combine like terms: -8 + -27 = -35 -35 + 29x + 3x + 12x2 = 27 + -3x + -27 + 3x Combine like terms: 29x + 3x = 32x -35 + 32x + 12x2 = 27 + -3x + -27 + 3x Reorder the terms: -35 + 32x + 12x2 = 27 + -27 + -3x + 3x Combine like terms: 27 + -27 = 0 -35 + 32x + 12x2 = 0 + -3x + 3x -35 + 32x + 12x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -35 + 32x + 12x2 = 0 Factor a trinomial. (-7 + -2x)(5 + -6x) = 0Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 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 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve: Simplifying 5 + -6x = 0 Solving 5 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6x = 0 + -5 -6x = 0 + -5 Combine like terms: 0 + -5 = -5 -6x = -5 Divide each side by '-6'. x = 0.8333333333 Simplifying x = 0.8333333333Solution
x = {-3.5, 0.8333333333}
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