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Simplifying (5x + 1)(7x + -4) = 0 Reorder the terms: (1 + 5x)(7x + -4) = 0 Reorder the terms: (1 + 5x)(-4 + 7x) = 0 Multiply (1 + 5x) * (-4 + 7x) (1(-4 + 7x) + 5x * (-4 + 7x)) = 0 ((-4 * 1 + 7x * 1) + 5x * (-4 + 7x)) = 0 ((-4 + 7x) + 5x * (-4 + 7x)) = 0 (-4 + 7x + (-4 * 5x + 7x * 5x)) = 0 (-4 + 7x + (-20x + 35x2)) = 0 Combine like terms: 7x + -20x = -13x (-4 + -13x + 35x2) = 0 Solving -4 + -13x + 35x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -5x)(4 + -7x) = 0Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve: Simplifying -1 + -5x = 0 Solving -1 + -5x = 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 + -5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x = 0 + 1 -5x = 0 + 1 Combine like terms: 0 + 1 = 1 -5x = 1 Divide each side by '-5'. x = -0.2 Simplifying x = -0.2Subproblem 2
Set the factor '(4 + -7x)' equal to zero and attempt to solve: Simplifying 4 + -7x = 0 Solving 4 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7x = 0 + -4 -7x = 0 + -4 Combine like terms: 0 + -4 = -4 -7x = -4 Divide each side by '-7'. x = 0.5714285714 Simplifying x = 0.5714285714Solution
x = {-0.2, 0.5714285714}
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