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Simplifying 5x(2x + 3) + 2x(3x + 1) = 0 Reorder the terms: 5x(3 + 2x) + 2x(3x + 1) = 0 (3 * 5x + 2x * 5x) + 2x(3x + 1) = 0 (15x + 10x2) + 2x(3x + 1) = 0 Reorder the terms: 15x + 10x2 + 2x(1 + 3x) = 0 15x + 10x2 + (1 * 2x + 3x * 2x) = 0 15x + 10x2 + (2x + 6x2) = 0 Reorder the terms: 15x + 2x + 10x2 + 6x2 = 0 Combine like terms: 15x + 2x = 17x 17x + 10x2 + 6x2 = 0 Combine like terms: 10x2 + 6x2 = 16x2 17x + 16x2 = 0 Solving 17x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(17 + 16x) = 0Subproblem 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 '(17 + 16x)' equal to zero and attempt to solve: Simplifying 17 + 16x = 0 Solving 17 + 16x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 16x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 16x = 0 + -17 16x = 0 + -17 Combine like terms: 0 + -17 = -17 16x = -17 Divide each side by '16'. x = -1.0625 Simplifying x = -1.0625Solution
x = {0, -1.0625}
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