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Simplifying (4x + 3)(-4x + 2) = 5(4x + 3) Reorder the terms: (3 + 4x)(-4x + 2) = 5(4x + 3) Reorder the terms: (3 + 4x)(2 + -4x) = 5(4x + 3) Multiply (3 + 4x) * (2 + -4x) (3(2 + -4x) + 4x * (2 + -4x)) = 5(4x + 3) ((2 * 3 + -4x * 3) + 4x * (2 + -4x)) = 5(4x + 3) ((6 + -12x) + 4x * (2 + -4x)) = 5(4x + 3) (6 + -12x + (2 * 4x + -4x * 4x)) = 5(4x + 3) (6 + -12x + (8x + -16x2)) = 5(4x + 3) Combine like terms: -12x + 8x = -4x (6 + -4x + -16x2) = 5(4x + 3) Reorder the terms: 6 + -4x + -16x2 = 5(3 + 4x) 6 + -4x + -16x2 = (3 * 5 + 4x * 5) 6 + -4x + -16x2 = (15 + 20x) Solving 6 + -4x + -16x2 = 15 + 20x Solving for variable 'x'. Reorder the terms: 6 + -15 + -4x + -20x + -16x2 = 15 + 20x + -15 + -20x Combine like terms: 6 + -15 = -9 -9 + -4x + -20x + -16x2 = 15 + 20x + -15 + -20x Combine like terms: -4x + -20x = -24x -9 + -24x + -16x2 = 15 + 20x + -15 + -20x Reorder the terms: -9 + -24x + -16x2 = 15 + -15 + 20x + -20x Combine like terms: 15 + -15 = 0 -9 + -24x + -16x2 = 0 + 20x + -20x -9 + -24x + -16x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -9 + -24x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 24x + 16x2) = 0 Factor a trinomial. -1((3 + 4x)(3 + 4x)) = 0 Ignore the factor -1.Subproblem 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 '(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 = -0.75Solution
x = {-0.75, -0.75}
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