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Simplifying (4x + 2)(5x + -7) = 0 Reorder the terms: (2 + 4x)(5x + -7) = 0 Reorder the terms: (2 + 4x)(-7 + 5x) = 0 Multiply (2 + 4x) * (-7 + 5x) (2(-7 + 5x) + 4x * (-7 + 5x)) = 0 ((-7 * 2 + 5x * 2) + 4x * (-7 + 5x)) = 0 ((-14 + 10x) + 4x * (-7 + 5x)) = 0 (-14 + 10x + (-7 * 4x + 5x * 4x)) = 0 (-14 + 10x + (-28x + 20x2)) = 0 Combine like terms: 10x + -28x = -18x (-14 + -18x + 20x2) = 0 Solving -14 + -18x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -9x + 10x2) = 0 Factor a trinomial. 2((-1 + -2x)(7 + -5x)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.5Subproblem 2
Set the factor '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4Solution
x = {-0.5, 1.4}
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