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Simplifying (2x + 7)(6x + 6) + (2x + 7)(x + -4) = 0 Reorder the terms: (7 + 2x)(6x + 6) + (2x + 7)(x + -4) = 0 Reorder the terms: (7 + 2x)(6 + 6x) + (2x + 7)(x + -4) = 0 Multiply (7 + 2x) * (6 + 6x) (7(6 + 6x) + 2x * (6 + 6x)) + (2x + 7)(x + -4) = 0 ((6 * 7 + 6x * 7) + 2x * (6 + 6x)) + (2x + 7)(x + -4) = 0 ((42 + 42x) + 2x * (6 + 6x)) + (2x + 7)(x + -4) = 0 (42 + 42x + (6 * 2x + 6x * 2x)) + (2x + 7)(x + -4) = 0 (42 + 42x + (12x + 12x2)) + (2x + 7)(x + -4) = 0 Combine like terms: 42x + 12x = 54x (42 + 54x + 12x2) + (2x + 7)(x + -4) = 0 Reorder the terms: 42 + 54x + 12x2 + (7 + 2x)(x + -4) = 0 Reorder the terms: 42 + 54x + 12x2 + (7 + 2x)(-4 + x) = 0 Multiply (7 + 2x) * (-4 + x) 42 + 54x + 12x2 + (7(-4 + x) + 2x * (-4 + x)) = 0 42 + 54x + 12x2 + ((-4 * 7 + x * 7) + 2x * (-4 + x)) = 0 42 + 54x + 12x2 + ((-28 + 7x) + 2x * (-4 + x)) = 0 42 + 54x + 12x2 + (-28 + 7x + (-4 * 2x + x * 2x)) = 0 42 + 54x + 12x2 + (-28 + 7x + (-8x + 2x2)) = 0 Combine like terms: 7x + -8x = -1x 42 + 54x + 12x2 + (-28 + -1x + 2x2) = 0 Reorder the terms: 42 + -28 + 54x + -1x + 12x2 + 2x2 = 0 Combine like terms: 42 + -28 = 14 14 + 54x + -1x + 12x2 + 2x2 = 0 Combine like terms: 54x + -1x = 53x 14 + 53x + 12x2 + 2x2 = 0 Combine like terms: 12x2 + 2x2 = 14x2 14 + 53x + 14x2 = 0 Solving 14 + 53x + 14x2 = 0 Solving for variable 'x'. Factor a trinomial. (7 + 2x)(2 + 7x) = 0Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 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 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Subproblem 2
Set the factor '(2 + 7x)' equal to zero and attempt to solve: Simplifying 2 + 7x = 0 Solving 2 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7x = 0 + -2 7x = 0 + -2 Combine like terms: 0 + -2 = -2 7x = -2 Divide each side by '7'. x = -0.2857142857 Simplifying x = -0.2857142857Solution
x = {-3.5, -0.2857142857}
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