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Simplifying (2x + 3)(2x + 3) + -1(2x + 3)(7x + -4) = 0 Reorder the terms: (3 + 2x)(2x + 3) + -1(2x + 3)(7x + -4) = 0 Reorder the terms: (3 + 2x)(3 + 2x) + -1(2x + 3)(7x + -4) = 0 Multiply (3 + 2x) * (3 + 2x) (3(3 + 2x) + 2x * (3 + 2x)) + -1(2x + 3)(7x + -4) = 0 ((3 * 3 + 2x * 3) + 2x * (3 + 2x)) + -1(2x + 3)(7x + -4) = 0 ((9 + 6x) + 2x * (3 + 2x)) + -1(2x + 3)(7x + -4) = 0 (9 + 6x + (3 * 2x + 2x * 2x)) + -1(2x + 3)(7x + -4) = 0 (9 + 6x + (6x + 4x2)) + -1(2x + 3)(7x + -4) = 0 Combine like terms: 6x + 6x = 12x (9 + 12x + 4x2) + -1(2x + 3)(7x + -4) = 0 Reorder the terms: 9 + 12x + 4x2 + -1(3 + 2x)(7x + -4) = 0 Reorder the terms: 9 + 12x + 4x2 + -1(3 + 2x)(-4 + 7x) = 0 Multiply (3 + 2x) * (-4 + 7x) 9 + 12x + 4x2 + -1(3(-4 + 7x) + 2x * (-4 + 7x)) = 0 9 + 12x + 4x2 + -1((-4 * 3 + 7x * 3) + 2x * (-4 + 7x)) = 0 9 + 12x + 4x2 + -1((-12 + 21x) + 2x * (-4 + 7x)) = 0 9 + 12x + 4x2 + -1(-12 + 21x + (-4 * 2x + 7x * 2x)) = 0 9 + 12x + 4x2 + -1(-12 + 21x + (-8x + 14x2)) = 0 Combine like terms: 21x + -8x = 13x 9 + 12x + 4x2 + -1(-12 + 13x + 14x2) = 0 9 + 12x + 4x2 + (-12 * -1 + 13x * -1 + 14x2 * -1) = 0 9 + 12x + 4x2 + (12 + -13x + -14x2) = 0 Reorder the terms: 9 + 12 + 12x + -13x + 4x2 + -14x2 = 0 Combine like terms: 9 + 12 = 21 21 + 12x + -13x + 4x2 + -14x2 = 0 Combine like terms: 12x + -13x = -1x 21 + -1x + 4x2 + -14x2 = 0 Combine like terms: 4x2 + -14x2 = -10x2 21 + -1x + -10x2 = 0 Solving 21 + -1x + -10x2 = 0 Solving for variable 'x'. Factor a trinomial. (7 + -5x)(3 + 2x) = 0Subproblem 1
Set the factor '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4Subproblem 2
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 = -1.5Solution
x = {1.4, -1.5}
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