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Simplifying 5x(3x + 2) + 3x(4x + -5) = 0 Reorder the terms: 5x(2 + 3x) + 3x(4x + -5) = 0 (2 * 5x + 3x * 5x) + 3x(4x + -5) = 0 (10x + 15x2) + 3x(4x + -5) = 0 Reorder the terms: 10x + 15x2 + 3x(-5 + 4x) = 0 10x + 15x2 + (-5 * 3x + 4x * 3x) = 0 10x + 15x2 + (-15x + 12x2) = 0 Reorder the terms: 10x + -15x + 15x2 + 12x2 = 0 Combine like terms: 10x + -15x = -5x -5x + 15x2 + 12x2 = 0 Combine like terms: 15x2 + 12x2 = 27x2 -5x + 27x2 = 0 Solving -5x + 27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 27x) = 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 '(-5 + 27x)' equal to zero and attempt to solve: Simplifying -5 + 27x = 0 Solving -5 + 27x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 27x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 27x = 0 + 5 27x = 0 + 5 Combine like terms: 0 + 5 = 5 27x = 5 Divide each side by '27'. x = 0.1851851852 Simplifying x = 0.1851851852Solution
x = {0, 0.1851851852}
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