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Simplifying (4x + 3)(x + -4) = 12x + 9 Reorder the terms: (3 + 4x)(x + -4) = 12x + 9 Reorder the terms: (3 + 4x)(-4 + x) = 12x + 9 Multiply (3 + 4x) * (-4 + x) (3(-4 + x) + 4x * (-4 + x)) = 12x + 9 ((-4 * 3 + x * 3) + 4x * (-4 + x)) = 12x + 9 ((-12 + 3x) + 4x * (-4 + x)) = 12x + 9 (-12 + 3x + (-4 * 4x + x * 4x)) = 12x + 9 (-12 + 3x + (-16x + 4x2)) = 12x + 9 Combine like terms: 3x + -16x = -13x (-12 + -13x + 4x2) = 12x + 9 Reorder the terms: -12 + -13x + 4x2 = 9 + 12x Solving -12 + -13x + 4x2 = 9 + 12x Solving for variable 'x'. Reorder the terms: -12 + -9 + -13x + -12x + 4x2 = 9 + 12x + -9 + -12x Combine like terms: -12 + -9 = -21 -21 + -13x + -12x + 4x2 = 9 + 12x + -9 + -12x Combine like terms: -13x + -12x = -25x -21 + -25x + 4x2 = 9 + 12x + -9 + -12x Reorder the terms: -21 + -25x + 4x2 = 9 + -9 + 12x + -12x Combine like terms: 9 + -9 = 0 -21 + -25x + 4x2 = 0 + 12x + -12x -21 + -25x + 4x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -21 + -25x + 4x2 = 0 Factor a trinomial. (-3 + -4x)(7 + -1x) = 0Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-0.75, 7}
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