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Simplifying (x + 6)(2x + -5) + (x + 6)(x + 9) = 0 Reorder the terms: (6 + x)(2x + -5) + (x + 6)(x + 9) = 0 Reorder the terms: (6 + x)(-5 + 2x) + (x + 6)(x + 9) = 0 Multiply (6 + x) * (-5 + 2x) (6(-5 + 2x) + x(-5 + 2x)) + (x + 6)(x + 9) = 0 ((-5 * 6 + 2x * 6) + x(-5 + 2x)) + (x + 6)(x + 9) = 0 ((-30 + 12x) + x(-5 + 2x)) + (x + 6)(x + 9) = 0 (-30 + 12x + (-5 * x + 2x * x)) + (x + 6)(x + 9) = 0 (-30 + 12x + (-5x + 2x2)) + (x + 6)(x + 9) = 0 Combine like terms: 12x + -5x = 7x (-30 + 7x + 2x2) + (x + 6)(x + 9) = 0 Reorder the terms: -30 + 7x + 2x2 + (6 + x)(x + 9) = 0 Reorder the terms: -30 + 7x + 2x2 + (6 + x)(9 + x) = 0 Multiply (6 + x) * (9 + x) -30 + 7x + 2x2 + (6(9 + x) + x(9 + x)) = 0 -30 + 7x + 2x2 + ((9 * 6 + x * 6) + x(9 + x)) = 0 -30 + 7x + 2x2 + ((54 + 6x) + x(9 + x)) = 0 -30 + 7x + 2x2 + (54 + 6x + (9 * x + x * x)) = 0 -30 + 7x + 2x2 + (54 + 6x + (9x + x2)) = 0 Combine like terms: 6x + 9x = 15x -30 + 7x + 2x2 + (54 + 15x + x2) = 0 Reorder the terms: -30 + 54 + 7x + 15x + 2x2 + x2 = 0 Combine like terms: -30 + 54 = 24 24 + 7x + 15x + 2x2 + x2 = 0 Combine like terms: 7x + 15x = 22x 24 + 22x + 2x2 + x2 = 0 Combine like terms: 2x2 + x2 = 3x2 24 + 22x + 3x2 = 0 Solving 24 + 22x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (6 + x)(4 + 3x) = 0Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333Solution
x = {-6, -1.333333333}
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