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Simplifying (3x + 1)(x + -1) + -1(x + 3)(x + -4) = x(x + 4) + 17 Reorder the terms: (1 + 3x)(x + -1) + -1(x + 3)(x + -4) = x(x + 4) + 17 Reorder the terms: (1 + 3x)(-1 + x) + -1(x + 3)(x + -4) = x(x + 4) + 17 Multiply (1 + 3x) * (-1 + x) (1(-1 + x) + 3x * (-1 + x)) + -1(x + 3)(x + -4) = x(x + 4) + 17 ((-1 * 1 + x * 1) + 3x * (-1 + x)) + -1(x + 3)(x + -4) = x(x + 4) + 17 ((-1 + 1x) + 3x * (-1 + x)) + -1(x + 3)(x + -4) = x(x + 4) + 17 (-1 + 1x + (-1 * 3x + x * 3x)) + -1(x + 3)(x + -4) = x(x + 4) + 17 (-1 + 1x + (-3x + 3x2)) + -1(x + 3)(x + -4) = x(x + 4) + 17 Combine like terms: 1x + -3x = -2x (-1 + -2x + 3x2) + -1(x + 3)(x + -4) = x(x + 4) + 17 Reorder the terms: -1 + -2x + 3x2 + -1(3 + x)(x + -4) = x(x + 4) + 17 Reorder the terms: -1 + -2x + 3x2 + -1(3 + x)(-4 + x) = x(x + 4) + 17 Multiply (3 + x) * (-4 + x) -1 + -2x + 3x2 + -1(3(-4 + x) + x(-4 + x)) = x(x + 4) + 17 -1 + -2x + 3x2 + -1((-4 * 3 + x * 3) + x(-4 + x)) = x(x + 4) + 17 -1 + -2x + 3x2 + -1((-12 + 3x) + x(-4 + x)) = x(x + 4) + 17 -1 + -2x + 3x2 + -1(-12 + 3x + (-4 * x + x * x)) = x(x + 4) + 17 -1 + -2x + 3x2 + -1(-12 + 3x + (-4x + x2)) = x(x + 4) + 17 Combine like terms: 3x + -4x = -1x -1 + -2x + 3x2 + -1(-12 + -1x + x2) = x(x + 4) + 17 -1 + -2x + 3x2 + (-12 * -1 + -1x * -1 + x2 * -1) = x(x + 4) + 17 -1 + -2x + 3x2 + (12 + 1x + -1x2) = x(x + 4) + 17 Reorder the terms: -1 + 12 + -2x + 1x + 3x2 + -1x2 = x(x + 4) + 17 Combine like terms: -1 + 12 = 11 11 + -2x + 1x + 3x2 + -1x2 = x(x + 4) + 17 Combine like terms: -2x + 1x = -1x 11 + -1x + 3x2 + -1x2 = x(x + 4) + 17 Combine like terms: 3x2 + -1x2 = 2x2 11 + -1x + 2x2 = x(x + 4) + 17 Reorder the terms: 11 + -1x + 2x2 = x(4 + x) + 17 11 + -1x + 2x2 = (4 * x + x * x) + 17 11 + -1x + 2x2 = (4x + x2) + 17 Reorder the terms: 11 + -1x + 2x2 = 17 + 4x + x2 Solving 11 + -1x + 2x2 = 17 + 4x + x2 Solving for variable 'x'. Reorder the terms: 11 + -17 + -1x + -4x + 2x2 + -1x2 = 17 + 4x + x2 + -17 + -4x + -1x2 Combine like terms: 11 + -17 = -6 -6 + -1x + -4x + 2x2 + -1x2 = 17 + 4x + x2 + -17 + -4x + -1x2 Combine like terms: -1x + -4x = -5x -6 + -5x + 2x2 + -1x2 = 17 + 4x + x2 + -17 + -4x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -6 + -5x + 1x2 = 17 + 4x + x2 + -17 + -4x + -1x2 Reorder the terms: -6 + -5x + 1x2 = 17 + -17 + 4x + -4x + x2 + -1x2 Combine like terms: 17 + -17 = 0 -6 + -5x + 1x2 = 0 + 4x + -4x + x2 + -1x2 -6 + -5x + 1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 -6 + -5x + 1x2 = 0 + x2 + -1x2 -6 + -5x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6 + -5x + 1x2 = 0 Factor a trinomial. (-1 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-1, 6}
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