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Simplifying (4x + 1)(7 + 5x) = 0 Reorder the terms: (1 + 4x)(7 + 5x) = 0 Multiply (1 + 4x) * (7 + 5x) (1(7 + 5x) + 4x * (7 + 5x)) = 0 ((7 * 1 + 5x * 1) + 4x * (7 + 5x)) = 0 ((7 + 5x) + 4x * (7 + 5x)) = 0 (7 + 5x + (7 * 4x + 5x * 4x)) = 0 (7 + 5x + (28x + 20x2)) = 0 Combine like terms: 5x + 28x = 33x (7 + 33x + 20x2) = 0 Solving 7 + 33x + 20x2 = 0 Solving for variable 'x'. Factor a trinomial. (7 + 5x)(1 + 4x) = 0Subproblem 1
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 = -1.4Subproblem 2
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 = -0.25Solution
x = {-1.4, -0.25}
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