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Simplifying (x + 4)(x + -1) = (2x + 1)(x + -1) Reorder the terms: (4 + x)(x + -1) = (2x + 1)(x + -1) Reorder the terms: (4 + x)(-1 + x) = (2x + 1)(x + -1) Multiply (4 + x) * (-1 + x) (4(-1 + x) + x(-1 + x)) = (2x + 1)(x + -1) ((-1 * 4 + x * 4) + x(-1 + x)) = (2x + 1)(x + -1) ((-4 + 4x) + x(-1 + x)) = (2x + 1)(x + -1) (-4 + 4x + (-1 * x + x * x)) = (2x + 1)(x + -1) (-4 + 4x + (-1x + x2)) = (2x + 1)(x + -1) Combine like terms: 4x + -1x = 3x (-4 + 3x + x2) = (2x + 1)(x + -1) Reorder the terms: -4 + 3x + x2 = (1 + 2x)(x + -1) Reorder the terms: -4 + 3x + x2 = (1 + 2x)(-1 + x) Multiply (1 + 2x) * (-1 + x) -4 + 3x + x2 = (1(-1 + x) + 2x * (-1 + x)) -4 + 3x + x2 = ((-1 * 1 + x * 1) + 2x * (-1 + x)) -4 + 3x + x2 = ((-1 + 1x) + 2x * (-1 + x)) -4 + 3x + x2 = (-1 + 1x + (-1 * 2x + x * 2x)) -4 + 3x + x2 = (-1 + 1x + (-2x + 2x2)) Combine like terms: 1x + -2x = -1x -4 + 3x + x2 = (-1 + -1x + 2x2) Solving -4 + 3x + x2 = -1 + -1x + 2x2 Solving for variable 'x'. Reorder the terms: -4 + 1 + 3x + x + x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2 Combine like terms: -4 + 1 = -3 -3 + 3x + x + x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2 Combine like terms: 3x + x = 4x -3 + 4x + x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -3 + 4x + -1x2 = -1 + -1x + 2x2 + 1 + x + -2x2 Reorder the terms: -3 + 4x + -1x2 = -1 + 1 + -1x + x + 2x2 + -2x2 Combine like terms: -1 + 1 = 0 -3 + 4x + -1x2 = 0 + -1x + x + 2x2 + -2x2 -3 + 4x + -1x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 -3 + 4x + -1x2 = 0 + 2x2 + -2x2 -3 + 4x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -3 + 4x + -1x2 = 0 Factor a trinomial. (-3 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
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 = 1Solution
x = {3, 1}
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