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