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Simplifying (3x + 1)(6x + -9) + -1(2x + -3)(2x + -3) = 0 Reorder the terms: (1 + 3x)(6x + -9) + -1(2x + -3)(2x + -3) = 0 Reorder the terms: (1 + 3x)(-9 + 6x) + -1(2x + -3)(2x + -3) = 0 Multiply (1 + 3x) * (-9 + 6x) (1(-9 + 6x) + 3x * (-9 + 6x)) + -1(2x + -3)(2x + -3) = 0 ((-9 * 1 + 6x * 1) + 3x * (-9 + 6x)) + -1(2x + -3)(2x + -3) = 0 ((-9 + 6x) + 3x * (-9 + 6x)) + -1(2x + -3)(2x + -3) = 0 (-9 + 6x + (-9 * 3x + 6x * 3x)) + -1(2x + -3)(2x + -3) = 0 (-9 + 6x + (-27x + 18x2)) + -1(2x + -3)(2x + -3) = 0 Combine like terms: 6x + -27x = -21x (-9 + -21x + 18x2) + -1(2x + -3)(2x + -3) = 0 Reorder the terms: -9 + -21x + 18x2 + -1(-3 + 2x)(2x + -3) = 0 Reorder the terms: -9 + -21x + 18x2 + -1(-3 + 2x)(-3 + 2x) = 0 Multiply (-3 + 2x) * (-3 + 2x) -9 + -21x + 18x2 + -1(-3(-3 + 2x) + 2x * (-3 + 2x)) = 0 -9 + -21x + 18x2 + -1((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 0 -9 + -21x + 18x2 + -1((9 + -6x) + 2x * (-3 + 2x)) = 0 -9 + -21x + 18x2 + -1(9 + -6x + (-3 * 2x + 2x * 2x)) = 0 -9 + -21x + 18x2 + -1(9 + -6x + (-6x + 4x2)) = 0 Combine like terms: -6x + -6x = -12x -9 + -21x + 18x2 + -1(9 + -12x + 4x2) = 0 -9 + -21x + 18x2 + (9 * -1 + -12x * -1 + 4x2 * -1) = 0 -9 + -21x + 18x2 + (-9 + 12x + -4x2) = 0 Reorder the terms: -9 + -9 + -21x + 12x + 18x2 + -4x2 = 0 Combine like terms: -9 + -9 = -18 -18 + -21x + 12x + 18x2 + -4x2 = 0 Combine like terms: -21x + 12x = -9x -18 + -9x + 18x2 + -4x2 = 0 Combine like terms: 18x2 + -4x2 = 14x2 -18 + -9x + 14x2 = 0 Solving -18 + -9x + 14x2 = 0 Solving for variable 'x'. Factor a trinomial. (-6 + -7x)(3 + -2x) = 0Subproblem 1
Set the factor '(-6 + -7x)' equal to zero and attempt to solve: Simplifying -6 + -7x = 0 Solving -6 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -7x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7x = 0 + 6 -7x = 0 + 6 Combine like terms: 0 + 6 = 6 -7x = 6 Divide each side by '-7'. x = -0.8571428571 Simplifying x = -0.8571428571Subproblem 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 = {-0.8571428571, 1.5}
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