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Simplifying (2x + 3)(4x + -5) = 0 Reorder the terms: (3 + 2x)(4x + -5) = 0 Reorder the terms: (3 + 2x)(-5 + 4x) = 0 Multiply (3 + 2x) * (-5 + 4x) (3(-5 + 4x) + 2x * (-5 + 4x)) = 0 ((-5 * 3 + 4x * 3) + 2x * (-5 + 4x)) = 0 ((-15 + 12x) + 2x * (-5 + 4x)) = 0 (-15 + 12x + (-5 * 2x + 4x * 2x)) = 0 (-15 + 12x + (-10x + 8x2)) = 0 Combine like terms: 12x + -10x = 2x (-15 + 2x + 8x2) = 0 Solving -15 + 2x + 8x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -2x)(5 + -4x) = 0Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 2
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 = 1.25Solution
x = {-1.5, 1.25}
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