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Simplifying (x + 7) * 2 = (x + 7)(3x + 4) Reorder the terms: (7 + x) * 2 = (x + 7)(3x + 4) Reorder the terms for easier multiplication: 2(7 + x) = (x + 7)(3x + 4) (7 * 2 + x * 2) = (x + 7)(3x + 4) (14 + 2x) = (x + 7)(3x + 4) Reorder the terms: 14 + 2x = (7 + x)(3x + 4) Reorder the terms: 14 + 2x = (7 + x)(4 + 3x) Multiply (7 + x) * (4 + 3x) 14 + 2x = (7(4 + 3x) + x(4 + 3x)) 14 + 2x = ((4 * 7 + 3x * 7) + x(4 + 3x)) 14 + 2x = ((28 + 21x) + x(4 + 3x)) 14 + 2x = (28 + 21x + (4 * x + 3x * x)) 14 + 2x = (28 + 21x + (4x + 3x2)) Combine like terms: 21x + 4x = 25x 14 + 2x = (28 + 25x + 3x2) Solving 14 + 2x = 28 + 25x + 3x2 Solving for variable 'x'. Reorder the terms: 14 + -28 + 2x + -25x + -3x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2 Combine like terms: 14 + -28 = -14 -14 + 2x + -25x + -3x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2 Combine like terms: 2x + -25x = -23x -14 + -23x + -3x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2 Reorder the terms: -14 + -23x + -3x2 = 28 + -28 + 25x + -25x + 3x2 + -3x2 Combine like terms: 28 + -28 = 0 -14 + -23x + -3x2 = 0 + 25x + -25x + 3x2 + -3x2 -14 + -23x + -3x2 = 25x + -25x + 3x2 + -3x2 Combine like terms: 25x + -25x = 0 -14 + -23x + -3x2 = 0 + 3x2 + -3x2 -14 + -23x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -14 + -23x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(14 + 23x + 3x2) = 0 Factor a trinomial. -1((7 + x)(2 + 3x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {-7, -0.6666666667}
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