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Simplifying (4x + 3)(x + -5) = 16x + 12 Reorder the terms: (3 + 4x)(x + -5) = 16x + 12 Reorder the terms: (3 + 4x)(-5 + x) = 16x + 12 Multiply (3 + 4x) * (-5 + x) (3(-5 + x) + 4x * (-5 + x)) = 16x + 12 ((-5 * 3 + x * 3) + 4x * (-5 + x)) = 16x + 12 ((-15 + 3x) + 4x * (-5 + x)) = 16x + 12 (-15 + 3x + (-5 * 4x + x * 4x)) = 16x + 12 (-15 + 3x + (-20x + 4x2)) = 16x + 12 Combine like terms: 3x + -20x = -17x (-15 + -17x + 4x2) = 16x + 12 Reorder the terms: -15 + -17x + 4x2 = 12 + 16x Solving -15 + -17x + 4x2 = 12 + 16x Solving for variable 'x'. Reorder the terms: -15 + -12 + -17x + -16x + 4x2 = 12 + 16x + -12 + -16x Combine like terms: -15 + -12 = -27 -27 + -17x + -16x + 4x2 = 12 + 16x + -12 + -16x Combine like terms: -17x + -16x = -33x -27 + -33x + 4x2 = 12 + 16x + -12 + -16x Reorder the terms: -27 + -33x + 4x2 = 12 + -12 + 16x + -16x Combine like terms: 12 + -12 = 0 -27 + -33x + 4x2 = 0 + 16x + -16x -27 + -33x + 4x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -27 + -33x + 4x2 = 0 Factor a trinomial. (-3 + -4x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 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 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-0.75, 9}
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