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Simplifying (-6x + 3)(-5 + -4x) = 0 Reorder the terms: (3 + -6x)(-5 + -4x) = 0 Multiply (3 + -6x) * (-5 + -4x) (3(-5 + -4x) + -6x * (-5 + -4x)) = 0 ((-5 * 3 + -4x * 3) + -6x * (-5 + -4x)) = 0 ((-15 + -12x) + -6x * (-5 + -4x)) = 0 (-15 + -12x + (-5 * -6x + -4x * -6x)) = 0 (-15 + -12x + (30x + 24x2)) = 0 Combine like terms: -12x + 30x = 18x (-15 + 18x + 24x2) = 0 Solving -15 + 18x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 6x + 8x2) = 0 Factor a trinomial. 3((-5 + -4x)(1 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve: Simplifying -5 + -4x = 0 Solving -5 + -4x = 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 + -4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4x = 0 + 5 -4x = 0 + 5 Combine like terms: 0 + 5 = 5 -4x = 5 Divide each side by '-4'. x = -1.25 Simplifying x = -1.25Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-1.25, 0.5}
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