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Simplifying (2x + 1)(3x + 2) = (4x + 2)(6x + 7) Reorder the terms: (1 + 2x)(3x + 2) = (4x + 2)(6x + 7) Reorder the terms: (1 + 2x)(2 + 3x) = (4x + 2)(6x + 7) Multiply (1 + 2x) * (2 + 3x) (1(2 + 3x) + 2x * (2 + 3x)) = (4x + 2)(6x + 7) ((2 * 1 + 3x * 1) + 2x * (2 + 3x)) = (4x + 2)(6x + 7) ((2 + 3x) + 2x * (2 + 3x)) = (4x + 2)(6x + 7) (2 + 3x + (2 * 2x + 3x * 2x)) = (4x + 2)(6x + 7) (2 + 3x + (4x + 6x2)) = (4x + 2)(6x + 7) Combine like terms: 3x + 4x = 7x (2 + 7x + 6x2) = (4x + 2)(6x + 7) Reorder the terms: 2 + 7x + 6x2 = (2 + 4x)(6x + 7) Reorder the terms: 2 + 7x + 6x2 = (2 + 4x)(7 + 6x) Multiply (2 + 4x) * (7 + 6x) 2 + 7x + 6x2 = (2(7 + 6x) + 4x * (7 + 6x)) 2 + 7x + 6x2 = ((7 * 2 + 6x * 2) + 4x * (7 + 6x)) 2 + 7x + 6x2 = ((14 + 12x) + 4x * (7 + 6x)) 2 + 7x + 6x2 = (14 + 12x + (7 * 4x + 6x * 4x)) 2 + 7x + 6x2 = (14 + 12x + (28x + 24x2)) Combine like terms: 12x + 28x = 40x 2 + 7x + 6x2 = (14 + 40x + 24x2) Solving 2 + 7x + 6x2 = 14 + 40x + 24x2 Solving for variable 'x'. Reorder the terms: 2 + -14 + 7x + -40x + 6x2 + -24x2 = 14 + 40x + 24x2 + -14 + -40x + -24x2 Combine like terms: 2 + -14 = -12 -12 + 7x + -40x + 6x2 + -24x2 = 14 + 40x + 24x2 + -14 + -40x + -24x2 Combine like terms: 7x + -40x = -33x -12 + -33x + 6x2 + -24x2 = 14 + 40x + 24x2 + -14 + -40x + -24x2 Combine like terms: 6x2 + -24x2 = -18x2 -12 + -33x + -18x2 = 14 + 40x + 24x2 + -14 + -40x + -24x2 Reorder the terms: -12 + -33x + -18x2 = 14 + -14 + 40x + -40x + 24x2 + -24x2 Combine like terms: 14 + -14 = 0 -12 + -33x + -18x2 = 0 + 40x + -40x + 24x2 + -24x2 -12 + -33x + -18x2 = 40x + -40x + 24x2 + -24x2 Combine like terms: 40x + -40x = 0 -12 + -33x + -18x2 = 0 + 24x2 + -24x2 -12 + -33x + -18x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -12 + -33x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(4 + 11x + 6x2) = 0 Factor a trinomial. -3((4 + 3x)(1 + 2x)) = 0 Ignore the factor -3.Subproblem 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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-1.333333333, -0.5}
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