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Simplifying (x + -3)(2x + 1) + (2x + 1)(3x + 4) = 0 Reorder the terms: (-3 + x)(2x + 1) + (2x + 1)(3x + 4) = 0 Reorder the terms: (-3 + x)(1 + 2x) + (2x + 1)(3x + 4) = 0 Multiply (-3 + x) * (1 + 2x) (-3(1 + 2x) + x(1 + 2x)) + (2x + 1)(3x + 4) = 0 ((1 * -3 + 2x * -3) + x(1 + 2x)) + (2x + 1)(3x + 4) = 0 ((-3 + -6x) + x(1 + 2x)) + (2x + 1)(3x + 4) = 0 (-3 + -6x + (1 * x + 2x * x)) + (2x + 1)(3x + 4) = 0 (-3 + -6x + (1x + 2x2)) + (2x + 1)(3x + 4) = 0 Combine like terms: -6x + 1x = -5x (-3 + -5x + 2x2) + (2x + 1)(3x + 4) = 0 Reorder the terms: -3 + -5x + 2x2 + (1 + 2x)(3x + 4) = 0 Reorder the terms: -3 + -5x + 2x2 + (1 + 2x)(4 + 3x) = 0 Multiply (1 + 2x) * (4 + 3x) -3 + -5x + 2x2 + (1(4 + 3x) + 2x * (4 + 3x)) = 0 -3 + -5x + 2x2 + ((4 * 1 + 3x * 1) + 2x * (4 + 3x)) = 0 -3 + -5x + 2x2 + ((4 + 3x) + 2x * (4 + 3x)) = 0 -3 + -5x + 2x2 + (4 + 3x + (4 * 2x + 3x * 2x)) = 0 -3 + -5x + 2x2 + (4 + 3x + (8x + 6x2)) = 0 Combine like terms: 3x + 8x = 11x -3 + -5x + 2x2 + (4 + 11x + 6x2) = 0 Reorder the terms: -3 + 4 + -5x + 11x + 2x2 + 6x2 = 0 Combine like terms: -3 + 4 = 1 1 + -5x + 11x + 2x2 + 6x2 = 0 Combine like terms: -5x + 11x = 6x 1 + 6x + 2x2 + 6x2 = 0 Combine like terms: 2x2 + 6x2 = 8x2 1 + 6x + 8x2 = 0 Solving 1 + 6x + 8x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + 2x)(1 + 4x) = 0Subproblem 1
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 = -0.5Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {-0.5, -0.25}
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