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Simplifying (4x + 6)(7x + 3) = 0 Reorder the terms: (6 + 4x)(7x + 3) = 0 Reorder the terms: (6 + 4x)(3 + 7x) = 0 Multiply (6 + 4x) * (3 + 7x) (6(3 + 7x) + 4x * (3 + 7x)) = 0 ((3 * 6 + 7x * 6) + 4x * (3 + 7x)) = 0 ((18 + 42x) + 4x * (3 + 7x)) = 0 (18 + 42x + (3 * 4x + 7x * 4x)) = 0 (18 + 42x + (12x + 28x2)) = 0 Combine like terms: 42x + 12x = 54x (18 + 54x + 28x2) = 0 Solving 18 + 54x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 27x + 14x2) = 0 Factor a trinomial. 2((3 + 2x)(3 + 7x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(3 + 7x)' equal to zero and attempt to solve: Simplifying 3 + 7x = 0 Solving 3 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 7x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7x = 0 + -3 7x = 0 + -3 Combine like terms: 0 + -3 = -3 7x = -3 Divide each side by '7'. x = -0.4285714286 Simplifying x = -0.4285714286Solution
x = {-1.5, -0.4285714286}
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