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Simplifying (3x + 4)(x + -4) = 12x + 16 Reorder the terms: (4 + 3x)(x + -4) = 12x + 16 Reorder the terms: (4 + 3x)(-4 + x) = 12x + 16 Multiply (4 + 3x) * (-4 + x) (4(-4 + x) + 3x * (-4 + x)) = 12x + 16 ((-4 * 4 + x * 4) + 3x * (-4 + x)) = 12x + 16 ((-16 + 4x) + 3x * (-4 + x)) = 12x + 16 (-16 + 4x + (-4 * 3x + x * 3x)) = 12x + 16 (-16 + 4x + (-12x + 3x2)) = 12x + 16 Combine like terms: 4x + -12x = -8x (-16 + -8x + 3x2) = 12x + 16 Reorder the terms: -16 + -8x + 3x2 = 16 + 12x Solving -16 + -8x + 3x2 = 16 + 12x Solving for variable 'x'. Reorder the terms: -16 + -16 + -8x + -12x + 3x2 = 16 + 12x + -16 + -12x Combine like terms: -16 + -16 = -32 -32 + -8x + -12x + 3x2 = 16 + 12x + -16 + -12x Combine like terms: -8x + -12x = -20x -32 + -20x + 3x2 = 16 + 12x + -16 + -12x Reorder the terms: -32 + -20x + 3x2 = 16 + -16 + 12x + -12x Combine like terms: 16 + -16 = 0 -32 + -20x + 3x2 = 0 + 12x + -12x -32 + -20x + 3x2 = 12x + -12x Combine like terms: 12x + -12x = 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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