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Simplifying (2x + 6)(5x + -3) = 0 Reorder the terms: (6 + 2x)(5x + -3) = 0 Reorder the terms: (6 + 2x)(-3 + 5x) = 0 Multiply (6 + 2x) * (-3 + 5x) (6(-3 + 5x) + 2x * (-3 + 5x)) = 0 ((-3 * 6 + 5x * 6) + 2x * (-3 + 5x)) = 0 ((-18 + 30x) + 2x * (-3 + 5x)) = 0 (-18 + 30x + (-3 * 2x + 5x * 2x)) = 0 (-18 + 30x + (-6x + 10x2)) = 0 Combine like terms: 30x + -6x = 24x (-18 + 24x + 10x2) = 0 Solving -18 + 24x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 12x + 5x2) = 0 Factor a trinomial. 2((-3 + -1x)(3 + -5x)) = 0 Ignore the factor 2.Subproblem 1
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 = -3Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 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 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6Solution
x = {-3, 0.6}
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