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Simplifying (2x + 3)(7x + 2) + -1(4x + 1)(2x + 3) = 0 Reorder the terms: (3 + 2x)(7x + 2) + -1(4x + 1)(2x + 3) = 0 Reorder the terms: (3 + 2x)(2 + 7x) + -1(4x + 1)(2x + 3) = 0 Multiply (3 + 2x) * (2 + 7x) (3(2 + 7x) + 2x * (2 + 7x)) + -1(4x + 1)(2x + 3) = 0 ((2 * 3 + 7x * 3) + 2x * (2 + 7x)) + -1(4x + 1)(2x + 3) = 0 ((6 + 21x) + 2x * (2 + 7x)) + -1(4x + 1)(2x + 3) = 0 (6 + 21x + (2 * 2x + 7x * 2x)) + -1(4x + 1)(2x + 3) = 0 (6 + 21x + (4x + 14x2)) + -1(4x + 1)(2x + 3) = 0 Combine like terms: 21x + 4x = 25x (6 + 25x + 14x2) + -1(4x + 1)(2x + 3) = 0 Reorder the terms: 6 + 25x + 14x2 + -1(1 + 4x)(2x + 3) = 0 Reorder the terms: 6 + 25x + 14x2 + -1(1 + 4x)(3 + 2x) = 0 Multiply (1 + 4x) * (3 + 2x) 6 + 25x + 14x2 + -1(1(3 + 2x) + 4x * (3 + 2x)) = 0 6 + 25x + 14x2 + -1((3 * 1 + 2x * 1) + 4x * (3 + 2x)) = 0 6 + 25x + 14x2 + -1((3 + 2x) + 4x * (3 + 2x)) = 0 6 + 25x + 14x2 + -1(3 + 2x + (3 * 4x + 2x * 4x)) = 0 6 + 25x + 14x2 + -1(3 + 2x + (12x + 8x2)) = 0 Combine like terms: 2x + 12x = 14x 6 + 25x + 14x2 + -1(3 + 14x + 8x2) = 0 6 + 25x + 14x2 + (3 * -1 + 14x * -1 + 8x2 * -1) = 0 6 + 25x + 14x2 + (-3 + -14x + -8x2) = 0 Reorder the terms: 6 + -3 + 25x + -14x + 14x2 + -8x2 = 0 Combine like terms: 6 + -3 = 3 3 + 25x + -14x + 14x2 + -8x2 = 0 Combine like terms: 25x + -14x = 11x 3 + 11x + 14x2 + -8x2 = 0 Combine like terms: 14x2 + -8x2 = 6x2 3 + 11x + 6x2 = 0 Solving 3 + 11x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + 2x)(1 + 3x) = 0Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-1.5, -0.3333333333}
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