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Simplifying (2x + 1)(x + 5) = (x + 11)(x + 3) Reorder the terms: (1 + 2x)(x + 5) = (x + 11)(x + 3) Reorder the terms: (1 + 2x)(5 + x) = (x + 11)(x + 3) Multiply (1 + 2x) * (5 + x) (1(5 + x) + 2x * (5 + x)) = (x + 11)(x + 3) ((5 * 1 + x * 1) + 2x * (5 + x)) = (x + 11)(x + 3) ((5 + 1x) + 2x * (5 + x)) = (x + 11)(x + 3) (5 + 1x + (5 * 2x + x * 2x)) = (x + 11)(x + 3) (5 + 1x + (10x + 2x2)) = (x + 11)(x + 3) Combine like terms: 1x + 10x = 11x (5 + 11x + 2x2) = (x + 11)(x + 3) Reorder the terms: 5 + 11x + 2x2 = (11 + x)(x + 3) Reorder the terms: 5 + 11x + 2x2 = (11 + x)(3 + x) Multiply (11 + x) * (3 + x) 5 + 11x + 2x2 = (11(3 + x) + x(3 + x)) 5 + 11x + 2x2 = ((3 * 11 + x * 11) + x(3 + x)) 5 + 11x + 2x2 = ((33 + 11x) + x(3 + x)) 5 + 11x + 2x2 = (33 + 11x + (3 * x + x * x)) 5 + 11x + 2x2 = (33 + 11x + (3x + x2)) Combine like terms: 11x + 3x = 14x 5 + 11x + 2x2 = (33 + 14x + x2) Solving 5 + 11x + 2x2 = 33 + 14x + x2 Solving for variable 'x'. Reorder the terms: 5 + -33 + 11x + -14x + 2x2 + -1x2 = 33 + 14x + x2 + -33 + -14x + -1x2 Combine like terms: 5 + -33 = -28 -28 + 11x + -14x + 2x2 + -1x2 = 33 + 14x + x2 + -33 + -14x + -1x2 Combine like terms: 11x + -14x = -3x -28 + -3x + 2x2 + -1x2 = 33 + 14x + x2 + -33 + -14x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -28 + -3x + 1x2 = 33 + 14x + x2 + -33 + -14x + -1x2 Reorder the terms: -28 + -3x + 1x2 = 33 + -33 + 14x + -14x + x2 + -1x2 Combine like terms: 33 + -33 = 0 -28 + -3x + 1x2 = 0 + 14x + -14x + x2 + -1x2 -28 + -3x + 1x2 = 14x + -14x + x2 + -1x2 Combine like terms: 14x + -14x = 0 -28 + -3x + 1x2 = 0 + x2 + -1x2 -28 + -3x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -28 + -3x + 1x2 = 0 Factor a trinomial. (-4 + -1x)(7 + -1x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-4, 7}
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