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Simplifying 6x(3x + -5) = 2x(9x + -6x) Reorder the terms: 6x(-5 + 3x) = 2x(9x + -6x) (-5 * 6x + 3x * 6x) = 2x(9x + -6x) (-30x + 18x2) = 2x(9x + -6x) Combine like terms: 9x + -6x = 3x -30x + 18x2 = 2x(3x) Remove parenthesis around (3x) -30x + 18x2 = 2x * 3x Reorder the terms for easier multiplication: -30x + 18x2 = 2 * 3x * x Multiply 2 * 3 -30x + 18x2 = 6x * x Multiply x * x -30x + 18x2 = 6x2 Solving -30x + 18x2 = 6x2 Solving for variable 'x'. Combine like terms: 18x2 + -6x2 = 12x2 -30x + 12x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -30x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '6x'. 6x(-5 + 2x) = 0 Ignore the factor 6.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 '(-5 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 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 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Divide each side by '2'. x = 2.5 Simplifying x = 2.5Solution
x = {0, 2.5}
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