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Simplifying (2x + 1)(4x + 5) = (2x + 1)(3x + 2) Reorder the terms: (1 + 2x)(4x + 5) = (2x + 1)(3x + 2) Reorder the terms: (1 + 2x)(5 + 4x) = (2x + 1)(3x + 2) Multiply (1 + 2x) * (5 + 4x) (1(5 + 4x) + 2x * (5 + 4x)) = (2x + 1)(3x + 2) ((5 * 1 + 4x * 1) + 2x * (5 + 4x)) = (2x + 1)(3x + 2) ((5 + 4x) + 2x * (5 + 4x)) = (2x + 1)(3x + 2) (5 + 4x + (5 * 2x + 4x * 2x)) = (2x + 1)(3x + 2) (5 + 4x + (10x + 8x2)) = (2x + 1)(3x + 2) Combine like terms: 4x + 10x = 14x (5 + 14x + 8x2) = (2x + 1)(3x + 2) Reorder the terms: 5 + 14x + 8x2 = (1 + 2x)(3x + 2) Reorder the terms: 5 + 14x + 8x2 = (1 + 2x)(2 + 3x) Multiply (1 + 2x) * (2 + 3x) 5 + 14x + 8x2 = (1(2 + 3x) + 2x * (2 + 3x)) 5 + 14x + 8x2 = ((2 * 1 + 3x * 1) + 2x * (2 + 3x)) 5 + 14x + 8x2 = ((2 + 3x) + 2x * (2 + 3x)) 5 + 14x + 8x2 = (2 + 3x + (2 * 2x + 3x * 2x)) 5 + 14x + 8x2 = (2 + 3x + (4x + 6x2)) Combine like terms: 3x + 4x = 7x 5 + 14x + 8x2 = (2 + 7x + 6x2) Solving 5 + 14x + 8x2 = 2 + 7x + 6x2 Solving for variable 'x'. Reorder the terms: 5 + -2 + 14x + -7x + 8x2 + -6x2 = 2 + 7x + 6x2 + -2 + -7x + -6x2 Combine like terms: 5 + -2 = 3 3 + 14x + -7x + 8x2 + -6x2 = 2 + 7x + 6x2 + -2 + -7x + -6x2 Combine like terms: 14x + -7x = 7x 3 + 7x + 8x2 + -6x2 = 2 + 7x + 6x2 + -2 + -7x + -6x2 Combine like terms: 8x2 + -6x2 = 2x2 3 + 7x + 2x2 = 2 + 7x + 6x2 + -2 + -7x + -6x2 Reorder the terms: 3 + 7x + 2x2 = 2 + -2 + 7x + -7x + 6x2 + -6x2 Combine like terms: 2 + -2 = 0 3 + 7x + 2x2 = 0 + 7x + -7x + 6x2 + -6x2 3 + 7x + 2x2 = 7x + -7x + 6x2 + -6x2 Combine like terms: 7x + -7x = 0 3 + 7x + 2x2 = 0 + 6x2 + -6x2 3 + 7x + 2x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 3 + 7x + 2x2 = 0 Factor a trinomial. (3 + x)(1 + 2x) = 0Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 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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