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Simplifying (5x + 3)(4x + -2) = 0 Reorder the terms: (3 + 5x)(4x + -2) = 0 Reorder the terms: (3 + 5x)(-2 + 4x) = 0 Multiply (3 + 5x) * (-2 + 4x) (3(-2 + 4x) + 5x * (-2 + 4x)) = 0 ((-2 * 3 + 4x * 3) + 5x * (-2 + 4x)) = 0 ((-6 + 12x) + 5x * (-2 + 4x)) = 0 (-6 + 12x + (-2 * 5x + 4x * 5x)) = 0 (-6 + 12x + (-10x + 20x2)) = 0 Combine like terms: 12x + -10x = 2x (-6 + 2x + 20x2) = 0 Solving -6 + 2x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + x + 10x2) = 0 Factor a trinomial. 2((-3 + -5x)(1 + -2x)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.6Subproblem 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 = {-0.6, 0.5}
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