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Simplifying (4x + -1)(2x + 5) = 0 Reorder the terms: (-1 + 4x)(2x + 5) = 0 Reorder the terms: (-1 + 4x)(5 + 2x) = 0 Multiply (-1 + 4x) * (5 + 2x) (-1(5 + 2x) + 4x * (5 + 2x)) = 0 ((5 * -1 + 2x * -1) + 4x * (5 + 2x)) = 0 ((-5 + -2x) + 4x * (5 + 2x)) = 0 (-5 + -2x + (5 * 4x + 2x * 4x)) = 0 (-5 + -2x + (20x + 8x2)) = 0 Combine like terms: -2x + 20x = 18x (-5 + 18x + 8x2) = 0 Solving -5 + 18x + 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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