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Simplifying (1 + 4x)(7x + -5) = 0 Reorder the terms: (1 + 4x)(-5 + 7x) = 0 Multiply (1 + 4x) * (-5 + 7x) (1(-5 + 7x) + 4x * (-5 + 7x)) = 0 ((-5 * 1 + 7x * 1) + 4x * (-5 + 7x)) = 0 ((-5 + 7x) + 4x * (-5 + 7x)) = 0 (-5 + 7x + (-5 * 4x + 7x * 4x)) = 0 (-5 + 7x + (-20x + 28x2)) = 0 Combine like terms: 7x + -20x = -13x (-5 + -13x + 28x2) = 0 Solving -5 + -13x + 28x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -4x)(5 + -7x) = 0Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve: Simplifying -1 + -4x = 0 Solving -1 + -4x = 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 + -4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x = 0 + 1 -4x = 0 + 1 Combine like terms: 0 + 1 = 1 -4x = 1 Divide each side by '-4'. x = -0.25 Simplifying x = -0.25Subproblem 2
Set the factor '(5 + -7x)' equal to zero and attempt to solve: Simplifying 5 + -7x = 0 Solving 5 + -7x = 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 + -7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7x = 0 + -5 -7x = 0 + -5 Combine like terms: 0 + -5 = -5 -7x = -5 Divide each side by '-7'. x = 0.7142857143 Simplifying x = 0.7142857143Solution
x = {-0.25, 0.7142857143}
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