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Simplifying (4x + 5)(1 + -1x) = 0 Reorder the terms: (5 + 4x)(1 + -1x) = 0 Multiply (5 + 4x) * (1 + -1x) (5(1 + -1x) + 4x * (1 + -1x)) = 0 ((1 * 5 + -1x * 5) + 4x * (1 + -1x)) = 0 ((5 + -5x) + 4x * (1 + -1x)) = 0 (5 + -5x + (1 * 4x + -1x * 4x)) = 0 (5 + -5x + (4x + -4x2)) = 0 Combine like terms: -5x + 4x = -1x (5 + -1x + -4x2) = 0 Solving 5 + -1x + -4x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x)(5 + 4x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 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 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Divide each side by '4'. x = -1.25 Simplifying x = -1.25Solution
x = {1, -1.25}
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