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Simplifying 5x + 7 = 2x + 3x(x + 9) + -20 Reorder the terms: 7 + 5x = 2x + 3x(x + 9) + -20 Reorder the terms: 7 + 5x = 2x + 3x(9 + x) + -20 7 + 5x = 2x + (9 * 3x + x * 3x) + -20 7 + 5x = 2x + (27x + 3x2) + -20 Reorder the terms: 7 + 5x = -20 + 2x + 27x + 3x2 Combine like terms: 2x + 27x = 29x 7 + 5x = -20 + 29x + 3x2 Solving 7 + 5x = -20 + 29x + 3x2 Solving for variable 'x'. Reorder the terms: 7 + 20 + 5x + -29x + -3x2 = -20 + 29x + 3x2 + 20 + -29x + -3x2 Combine like terms: 7 + 20 = 27 27 + 5x + -29x + -3x2 = -20 + 29x + 3x2 + 20 + -29x + -3x2 Combine like terms: 5x + -29x = -24x 27 + -24x + -3x2 = -20 + 29x + 3x2 + 20 + -29x + -3x2 Reorder the terms: 27 + -24x + -3x2 = -20 + 20 + 29x + -29x + 3x2 + -3x2 Combine like terms: -20 + 20 = 0 27 + -24x + -3x2 = 0 + 29x + -29x + 3x2 + -3x2 27 + -24x + -3x2 = 29x + -29x + 3x2 + -3x2 Combine like terms: 29x + -29x = 0 27 + -24x + -3x2 = 0 + 3x2 + -3x2 27 + -24x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 27 + -24x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -8x + -1x2) = 0 Factor a trinomial. 3((1 + -1x)(9 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Solution
x = {1, -9}
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