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Simplifying 5x(5x + 3) + 2x(3x + 8) = 0 Reorder the terms: 5x(3 + 5x) + 2x(3x + 8) = 0 (3 * 5x + 5x * 5x) + 2x(3x + 8) = 0 (15x + 25x2) + 2x(3x + 8) = 0 Reorder the terms: 15x + 25x2 + 2x(8 + 3x) = 0 15x + 25x2 + (8 * 2x + 3x * 2x) = 0 15x + 25x2 + (16x + 6x2) = 0 Reorder the terms: 15x + 16x + 25x2 + 6x2 = 0 Combine like terms: 15x + 16x = 31x 31x + 25x2 + 6x2 = 0 Combine like terms: 25x2 + 6x2 = 31x2 31x + 31x2 = 0 Solving 31x + 31x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '31x'. 31x(1 + x) = 0 Ignore the factor 31.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {0, -1}
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