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Simplifying (2x + -1)(x + -5) = x(x + -5) Reorder the terms: (-1 + 2x)(x + -5) = x(x + -5) Reorder the terms: (-1 + 2x)(-5 + x) = x(x + -5) Multiply (-1 + 2x) * (-5 + x) (-1(-5 + x) + 2x * (-5 + x)) = x(x + -5) ((-5 * -1 + x * -1) + 2x * (-5 + x)) = x(x + -5) ((5 + -1x) + 2x * (-5 + x)) = x(x + -5) (5 + -1x + (-5 * 2x + x * 2x)) = x(x + -5) (5 + -1x + (-10x + 2x2)) = x(x + -5) Combine like terms: -1x + -10x = -11x (5 + -11x + 2x2) = x(x + -5) Reorder the terms: 5 + -11x + 2x2 = x(-5 + x) 5 + -11x + 2x2 = (-5 * x + x * x) 5 + -11x + 2x2 = (-5x + x2) Solving 5 + -11x + 2x2 = -5x + x2 Solving for variable 'x'. Reorder the terms: 5 + -11x + 5x + 2x2 + -1x2 = -5x + x2 + 5x + -1x2 Combine like terms: -11x + 5x = -6x 5 + -6x + 2x2 + -1x2 = -5x + x2 + 5x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 5 + -6x + 1x2 = -5x + x2 + 5x + -1x2 Reorder the terms: 5 + -6x + 1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 5 + -6x + 1x2 = 0 + x2 + -1x2 5 + -6x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + -6x + 1x2 = 0 Factor a trinomial. (1 + -1x)(5 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {1, 5}
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