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Simplifying (3x + 6)(14x + 10) + (4x + 8)(3x + 6) = 0 Reorder the terms: (6 + 3x)(14x + 10) + (4x + 8)(3x + 6) = 0 Reorder the terms: (6 + 3x)(10 + 14x) + (4x + 8)(3x + 6) = 0 Multiply (6 + 3x) * (10 + 14x) (6(10 + 14x) + 3x * (10 + 14x)) + (4x + 8)(3x + 6) = 0 ((10 * 6 + 14x * 6) + 3x * (10 + 14x)) + (4x + 8)(3x + 6) = 0 ((60 + 84x) + 3x * (10 + 14x)) + (4x + 8)(3x + 6) = 0 (60 + 84x + (10 * 3x + 14x * 3x)) + (4x + 8)(3x + 6) = 0 (60 + 84x + (30x + 42x2)) + (4x + 8)(3x + 6) = 0 Combine like terms: 84x + 30x = 114x (60 + 114x + 42x2) + (4x + 8)(3x + 6) = 0 Reorder the terms: 60 + 114x + 42x2 + (8 + 4x)(3x + 6) = 0 Reorder the terms: 60 + 114x + 42x2 + (8 + 4x)(6 + 3x) = 0 Multiply (8 + 4x) * (6 + 3x) 60 + 114x + 42x2 + (8(6 + 3x) + 4x * (6 + 3x)) = 0 60 + 114x + 42x2 + ((6 * 8 + 3x * 8) + 4x * (6 + 3x)) = 0 60 + 114x + 42x2 + ((48 + 24x) + 4x * (6 + 3x)) = 0 60 + 114x + 42x2 + (48 + 24x + (6 * 4x + 3x * 4x)) = 0 60 + 114x + 42x2 + (48 + 24x + (24x + 12x2)) = 0 Combine like terms: 24x + 24x = 48x 60 + 114x + 42x2 + (48 + 48x + 12x2) = 0 Reorder the terms: 60 + 48 + 114x + 48x + 42x2 + 12x2 = 0 Combine like terms: 60 + 48 = 108 108 + 114x + 48x + 42x2 + 12x2 = 0 Combine like terms: 114x + 48x = 162x 108 + 162x + 42x2 + 12x2 = 0 Combine like terms: 42x2 + 12x2 = 54x2 108 + 162x + 54x2 = 0 Solving 108 + 162x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '54'. 54(2 + 3x + x2) = 0 Factor a trinomial. 54((2 + x)(1 + x)) = 0 Ignore the factor 54.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-2, -1}
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