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Simplifying (6x + 3)(7x + 4) = 0 Reorder the terms: (3 + 6x)(7x + 4) = 0 Reorder the terms: (3 + 6x)(4 + 7x) = 0 Multiply (3 + 6x) * (4 + 7x) (3(4 + 7x) + 6x * (4 + 7x)) = 0 ((4 * 3 + 7x * 3) + 6x * (4 + 7x)) = 0 ((12 + 21x) + 6x * (4 + 7x)) = 0 (12 + 21x + (4 * 6x + 7x * 6x)) = 0 (12 + 21x + (24x + 42x2)) = 0 Combine like terms: 21x + 24x = 45x (12 + 45x + 42x2) = 0 Solving 12 + 45x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 15x + 14x2) = 0 Factor a trinomial. 3((4 + 7x)(1 + 2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 7x)' equal to zero and attempt to solve: Simplifying 4 + 7x = 0 Solving 4 + 7x = 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 + 7x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7x = 0 + -4 7x = 0 + -4 Combine like terms: 0 + -4 = -4 7x = -4 Divide each side by '7'. x = -0.5714285714 Simplifying x = -0.5714285714Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-0.5714285714, -0.5}
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