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Simplifying 6x(x + -3)(2x + 5) = 0 Reorder the terms: 6x(-3 + x)(2x + 5) = 0 Reorder the terms: 6x(-3 + x)(5 + 2x) = 0 Multiply (-3 + x) * (5 + 2x) 6x(-3(5 + 2x) + x(5 + 2x)) = 0 6x((5 * -3 + 2x * -3) + x(5 + 2x)) = 0 6x((-15 + -6x) + x(5 + 2x)) = 0 6x(-15 + -6x + (5 * x + 2x * x)) = 0 6x(-15 + -6x + (5x + 2x2)) = 0 Combine like terms: -6x + 5x = -1x 6x(-15 + -1x + 2x2) = 0 (-15 * 6x + -1x * 6x + 2x2 * 6x) = 0 (-90x + -6x2 + 12x3) = 0 Solving -90x + -6x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(-15 + -1x + 2x2) = 0 Factor a trinomial. 6x((-5 + -2x)(3 + -1x)) = 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 = -2.5Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0, -2.5, 3}
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