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Simplifying (x + 4)(x + 6) + -1(8x + -5)(x + 6) = 0 Reorder the terms: (4 + x)(x + 6) + -1(8x + -5)(x + 6) = 0 Reorder the terms: (4 + x)(6 + x) + -1(8x + -5)(x + 6) = 0 Multiply (4 + x) * (6 + x) (4(6 + x) + x(6 + x)) + -1(8x + -5)(x + 6) = 0 ((6 * 4 + x * 4) + x(6 + x)) + -1(8x + -5)(x + 6) = 0 ((24 + 4x) + x(6 + x)) + -1(8x + -5)(x + 6) = 0 (24 + 4x + (6 * x + x * x)) + -1(8x + -5)(x + 6) = 0 (24 + 4x + (6x + x2)) + -1(8x + -5)(x + 6) = 0 Combine like terms: 4x + 6x = 10x (24 + 10x + x2) + -1(8x + -5)(x + 6) = 0 Reorder the terms: 24 + 10x + x2 + -1(-5 + 8x)(x + 6) = 0 Reorder the terms: 24 + 10x + x2 + -1(-5 + 8x)(6 + x) = 0 Multiply (-5 + 8x) * (6 + x) 24 + 10x + x2 + -1(-5(6 + x) + 8x * (6 + x)) = 0 24 + 10x + x2 + -1((6 * -5 + x * -5) + 8x * (6 + x)) = 0 24 + 10x + x2 + -1((-30 + -5x) + 8x * (6 + x)) = 0 24 + 10x + x2 + -1(-30 + -5x + (6 * 8x + x * 8x)) = 0 24 + 10x + x2 + -1(-30 + -5x + (48x + 8x2)) = 0 Combine like terms: -5x + 48x = 43x 24 + 10x + x2 + -1(-30 + 43x + 8x2) = 0 24 + 10x + x2 + (-30 * -1 + 43x * -1 + 8x2 * -1) = 0 24 + 10x + x2 + (30 + -43x + -8x2) = 0 Reorder the terms: 24 + 30 + 10x + -43x + x2 + -8x2 = 0 Combine like terms: 24 + 30 = 54 54 + 10x + -43x + x2 + -8x2 = 0 Combine like terms: 10x + -43x = -33x 54 + -33x + x2 + -8x2 = 0 Combine like terms: x2 + -8x2 = -7x2 54 + -33x + -7x2 = 0 Solving 54 + -33x + -7x2 = 0 Solving for variable 'x'. Factor a trinomial. (9 + -7x)(6 + x) = 0Subproblem 1
Set the factor '(9 + -7x)' equal to zero and attempt to solve: Simplifying 9 + -7x = 0 Solving 9 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -7x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7x = 0 + -9 -7x = 0 + -9 Combine like terms: 0 + -9 = -9 -7x = -9 Divide each side by '-7'. x = 1.285714286 Simplifying x = 1.285714286Subproblem 2
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 = -6Solution
x = {1.285714286, -6}
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