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Simplifying (2x + -1)(4x + 5) = (2x + -1)(6 + -1x) Reorder the terms: (-1 + 2x)(4x + 5) = (2x + -1)(6 + -1x) Reorder the terms: (-1 + 2x)(5 + 4x) = (2x + -1)(6 + -1x) Multiply (-1 + 2x) * (5 + 4x) (-1(5 + 4x) + 2x * (5 + 4x)) = (2x + -1)(6 + -1x) ((5 * -1 + 4x * -1) + 2x * (5 + 4x)) = (2x + -1)(6 + -1x) ((-5 + -4x) + 2x * (5 + 4x)) = (2x + -1)(6 + -1x) (-5 + -4x + (5 * 2x + 4x * 2x)) = (2x + -1)(6 + -1x) (-5 + -4x + (10x + 8x2)) = (2x + -1)(6 + -1x) Combine like terms: -4x + 10x = 6x (-5 + 6x + 8x2) = (2x + -1)(6 + -1x) Reorder the terms: -5 + 6x + 8x2 = (-1 + 2x)(6 + -1x) Multiply (-1 + 2x) * (6 + -1x) -5 + 6x + 8x2 = (-1(6 + -1x) + 2x * (6 + -1x)) -5 + 6x + 8x2 = ((6 * -1 + -1x * -1) + 2x * (6 + -1x)) -5 + 6x + 8x2 = ((-6 + 1x) + 2x * (6 + -1x)) -5 + 6x + 8x2 = (-6 + 1x + (6 * 2x + -1x * 2x)) -5 + 6x + 8x2 = (-6 + 1x + (12x + -2x2)) Combine like terms: 1x + 12x = 13x -5 + 6x + 8x2 = (-6 + 13x + -2x2) Solving -5 + 6x + 8x2 = -6 + 13x + -2x2 Solving for variable 'x'. Reorder the terms: -5 + 6 + 6x + -13x + 8x2 + 2x2 = -6 + 13x + -2x2 + 6 + -13x + 2x2 Combine like terms: -5 + 6 = 1 1 + 6x + -13x + 8x2 + 2x2 = -6 + 13x + -2x2 + 6 + -13x + 2x2 Combine like terms: 6x + -13x = -7x 1 + -7x + 8x2 + 2x2 = -6 + 13x + -2x2 + 6 + -13x + 2x2 Combine like terms: 8x2 + 2x2 = 10x2 1 + -7x + 10x2 = -6 + 13x + -2x2 + 6 + -13x + 2x2 Reorder the terms: 1 + -7x + 10x2 = -6 + 6 + 13x + -13x + -2x2 + 2x2 Combine like terms: -6 + 6 = 0 1 + -7x + 10x2 = 0 + 13x + -13x + -2x2 + 2x2 1 + -7x + 10x2 = 13x + -13x + -2x2 + 2x2 Combine like terms: 13x + -13x = 0 1 + -7x + 10x2 = 0 + -2x2 + 2x2 1 + -7x + 10x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 1 + -7x + 10x2 = 0 Factor a trinomial. (1 + -5x)(1 + -2x) = 0Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {0.2, 0.5}
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