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Simplifying (10 + -4x)(7x + 3) = 0 Reorder the terms: (10 + -4x)(3 + 7x) = 0 Multiply (10 + -4x) * (3 + 7x) (10(3 + 7x) + -4x * (3 + 7x)) = 0 ((3 * 10 + 7x * 10) + -4x * (3 + 7x)) = 0 ((30 + 70x) + -4x * (3 + 7x)) = 0 (30 + 70x + (3 * -4x + 7x * -4x)) = 0 (30 + 70x + (-12x + -28x2)) = 0 Combine like terms: 70x + -12x = 58x (30 + 58x + -28x2) = 0 Solving 30 + 58x + -28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 29x + -14x2) = 0 Factor a trinomial. 2((5 + -2x)(3 + 7x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Subproblem 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 = {2.5, -0.4285714286}
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