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Simplifying (6x + 2)(2x + 3) = (4x + 6)(4x + 7) Reorder the terms: (2 + 6x)(2x + 3) = (4x + 6)(4x + 7) Reorder the terms: (2 + 6x)(3 + 2x) = (4x + 6)(4x + 7) Multiply (2 + 6x) * (3 + 2x) (2(3 + 2x) + 6x * (3 + 2x)) = (4x + 6)(4x + 7) ((3 * 2 + 2x * 2) + 6x * (3 + 2x)) = (4x + 6)(4x + 7) ((6 + 4x) + 6x * (3 + 2x)) = (4x + 6)(4x + 7) (6 + 4x + (3 * 6x + 2x * 6x)) = (4x + 6)(4x + 7) (6 + 4x + (18x + 12x2)) = (4x + 6)(4x + 7) Combine like terms: 4x + 18x = 22x (6 + 22x + 12x2) = (4x + 6)(4x + 7) Reorder the terms: 6 + 22x + 12x2 = (6 + 4x)(4x + 7) Reorder the terms: 6 + 22x + 12x2 = (6 + 4x)(7 + 4x) Multiply (6 + 4x) * (7 + 4x) 6 + 22x + 12x2 = (6(7 + 4x) + 4x * (7 + 4x)) 6 + 22x + 12x2 = ((7 * 6 + 4x * 6) + 4x * (7 + 4x)) 6 + 22x + 12x2 = ((42 + 24x) + 4x * (7 + 4x)) 6 + 22x + 12x2 = (42 + 24x + (7 * 4x + 4x * 4x)) 6 + 22x + 12x2 = (42 + 24x + (28x + 16x2)) Combine like terms: 24x + 28x = 52x 6 + 22x + 12x2 = (42 + 52x + 16x2) Solving 6 + 22x + 12x2 = 42 + 52x + 16x2 Solving for variable 'x'. Reorder the terms: 6 + -42 + 22x + -52x + 12x2 + -16x2 = 42 + 52x + 16x2 + -42 + -52x + -16x2 Combine like terms: 6 + -42 = -36 -36 + 22x + -52x + 12x2 + -16x2 = 42 + 52x + 16x2 + -42 + -52x + -16x2 Combine like terms: 22x + -52x = -30x -36 + -30x + 12x2 + -16x2 = 42 + 52x + 16x2 + -42 + -52x + -16x2 Combine like terms: 12x2 + -16x2 = -4x2 -36 + -30x + -4x2 = 42 + 52x + 16x2 + -42 + -52x + -16x2 Reorder the terms: -36 + -30x + -4x2 = 42 + -42 + 52x + -52x + 16x2 + -16x2 Combine like terms: 42 + -42 = 0 -36 + -30x + -4x2 = 0 + 52x + -52x + 16x2 + -16x2 -36 + -30x + -4x2 = 52x + -52x + 16x2 + -16x2 Combine like terms: 52x + -52x = 0 -36 + -30x + -4x2 = 0 + 16x2 + -16x2 -36 + -30x + -4x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -36 + -30x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(18 + 15x + 2x2) = 0 Factor a trinomial. -2((6 + x)(3 + 2x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {-6, -1.5}
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