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Simplifying (2x + 5)(4x + 1) = 0 Reorder the terms: (5 + 2x)(4x + 1) = 0 Reorder the terms: (5 + 2x)(1 + 4x) = 0 Multiply (5 + 2x) * (1 + 4x) (5(1 + 4x) + 2x * (1 + 4x)) = 0 ((1 * 5 + 4x * 5) + 2x * (1 + 4x)) = 0 ((5 + 20x) + 2x * (1 + 4x)) = 0 (5 + 20x + (1 * 2x + 4x * 2x)) = 0 (5 + 20x + (2x + 8x2)) = 0 Combine like terms: 20x + 2x = 22x (5 + 22x + 8x2) = 0 Solving 5 + 22x + 8x2 = 0 Solving for variable 'x'. Factor a trinomial. (5 + 2x)(1 + 4x) = 0Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 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 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 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 = {-2.5, -0.25}
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