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Simplifying x(x + 1)(x + 2) + 11 = (x2 + 1)(x + 5) Reorder the terms: x(1 + x)(x + 2) + 11 = (x2 + 1)(x + 5) Reorder the terms: x(1 + x)(2 + x) + 11 = (x2 + 1)(x + 5) Multiply (1 + x) * (2 + x) x(1(2 + x) + x(2 + x)) + 11 = (x2 + 1)(x + 5) x((2 * 1 + x * 1) + x(2 + x)) + 11 = (x2 + 1)(x + 5) x((2 + 1x) + x(2 + x)) + 11 = (x2 + 1)(x + 5) x(2 + 1x + (2 * x + x * x)) + 11 = (x2 + 1)(x + 5) x(2 + 1x + (2x + x2)) + 11 = (x2 + 1)(x + 5) Combine like terms: 1x + 2x = 3x x(2 + 3x + x2) + 11 = (x2 + 1)(x + 5) (2 * x + 3x * x + x2 * x) + 11 = (x2 + 1)(x + 5) (2x + 3x2 + x3) + 11 = (x2 + 1)(x + 5) Reorder the terms: 11 + 2x + 3x2 + x3 = (x2 + 1)(x + 5) Reorder the terms: 11 + 2x + 3x2 + x3 = (1 + x2)(x + 5) Reorder the terms: 11 + 2x + 3x2 + x3 = (1 + x2)(5 + x) Multiply (1 + x2) * (5 + x) 11 + 2x + 3x2 + x3 = (1(5 + x) + x2(5 + x)) 11 + 2x + 3x2 + x3 = ((5 * 1 + x * 1) + x2(5 + x)) 11 + 2x + 3x2 + x3 = ((5 + 1x) + x2(5 + x)) 11 + 2x + 3x2 + x3 = (5 + 1x + (5 * x2 + x * x2)) 11 + 2x + 3x2 + x3 = (5 + 1x + (5x2 + x3)) 11 + 2x + 3x2 + x3 = (5 + 1x + 5x2 + x3) Add '-1x3' to each side of the equation. 11 + 2x + 3x2 + x3 + -1x3 = 5 + 1x + 5x2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 11 + 2x + 3x2 + 0 = 5 + 1x + 5x2 + x3 + -1x3 11 + 2x + 3x2 = 5 + 1x + 5x2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 11 + 2x + 3x2 = 5 + 1x + 5x2 + 0 11 + 2x + 3x2 = 5 + 1x + 5x2 Solving 11 + 2x + 3x2 = 5 + 1x + 5x2 Solving for variable 'x'. Reorder the terms: 11 + -5 + 2x + -1x + 3x2 + -5x2 = 5 + 1x + 5x2 + -5 + -1x + -5x2 Combine like terms: 11 + -5 = 6 6 + 2x + -1x + 3x2 + -5x2 = 5 + 1x + 5x2 + -5 + -1x + -5x2 Combine like terms: 2x + -1x = 1x 6 + 1x + 3x2 + -5x2 = 5 + 1x + 5x2 + -5 + -1x + -5x2 Combine like terms: 3x2 + -5x2 = -2x2 6 + 1x + -2x2 = 5 + 1x + 5x2 + -5 + -1x + -5x2 Reorder the terms: 6 + 1x + -2x2 = 5 + -5 + 1x + -1x + 5x2 + -5x2 Combine like terms: 5 + -5 = 0 6 + 1x + -2x2 = 0 + 1x + -1x + 5x2 + -5x2 6 + 1x + -2x2 = 1x + -1x + 5x2 + -5x2 Combine like terms: 1x + -1x = 0 6 + 1x + -2x2 = 0 + 5x2 + -5x2 6 + 1x + -2x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 6 + 1x + -2x2 = 0 Factor a trinomial. (2 + -1x)(3 + 2x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {2, -1.5}
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