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Simplifying (x + 4)(2x + 1) = (2x + 5)(2 + -1x) Reorder the terms: (4 + x)(2x + 1) = (2x + 5)(2 + -1x) Reorder the terms: (4 + x)(1 + 2x) = (2x + 5)(2 + -1x) Multiply (4 + x) * (1 + 2x) (4(1 + 2x) + x(1 + 2x)) = (2x + 5)(2 + -1x) ((1 * 4 + 2x * 4) + x(1 + 2x)) = (2x + 5)(2 + -1x) ((4 + 8x) + x(1 + 2x)) = (2x + 5)(2 + -1x) (4 + 8x + (1 * x + 2x * x)) = (2x + 5)(2 + -1x) (4 + 8x + (1x + 2x2)) = (2x + 5)(2 + -1x) Combine like terms: 8x + 1x = 9x (4 + 9x + 2x2) = (2x + 5)(2 + -1x) Reorder the terms: 4 + 9x + 2x2 = (5 + 2x)(2 + -1x) Multiply (5 + 2x) * (2 + -1x) 4 + 9x + 2x2 = (5(2 + -1x) + 2x * (2 + -1x)) 4 + 9x + 2x2 = ((2 * 5 + -1x * 5) + 2x * (2 + -1x)) 4 + 9x + 2x2 = ((10 + -5x) + 2x * (2 + -1x)) 4 + 9x + 2x2 = (10 + -5x + (2 * 2x + -1x * 2x)) 4 + 9x + 2x2 = (10 + -5x + (4x + -2x2)) Combine like terms: -5x + 4x = -1x 4 + 9x + 2x2 = (10 + -1x + -2x2) Solving 4 + 9x + 2x2 = 10 + -1x + -2x2 Solving for variable 'x'. Reorder the terms: 4 + -10 + 9x + x + 2x2 + 2x2 = 10 + -1x + -2x2 + -10 + x + 2x2 Combine like terms: 4 + -10 = -6 -6 + 9x + x + 2x2 + 2x2 = 10 + -1x + -2x2 + -10 + x + 2x2 Combine like terms: 9x + x = 10x -6 + 10x + 2x2 + 2x2 = 10 + -1x + -2x2 + -10 + x + 2x2 Combine like terms: 2x2 + 2x2 = 4x2 -6 + 10x + 4x2 = 10 + -1x + -2x2 + -10 + x + 2x2 Reorder the terms: -6 + 10x + 4x2 = 10 + -10 + -1x + x + -2x2 + 2x2 Combine like terms: 10 + -10 = 0 -6 + 10x + 4x2 = 0 + -1x + x + -2x2 + 2x2 -6 + 10x + 4x2 = -1x + x + -2x2 + 2x2 Combine like terms: -1x + x = 0 -6 + 10x + 4x2 = 0 + -2x2 + 2x2 -6 + 10x + 4x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -6 + 10x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 5x + 2x2) = 0 Factor a trinomial. 2((-3 + -1x)(1 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 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 = {-3, 0.5}
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