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Simplifying (-5x + 10)(7x + -3) = 0 Reorder the terms: (10 + -5x)(7x + -3) = 0 Reorder the terms: (10 + -5x)(-3 + 7x) = 0 Multiply (10 + -5x) * (-3 + 7x) (10(-3 + 7x) + -5x * (-3 + 7x)) = 0 ((-3 * 10 + 7x * 10) + -5x * (-3 + 7x)) = 0 ((-30 + 70x) + -5x * (-3 + 7x)) = 0 (-30 + 70x + (-3 * -5x + 7x * -5x)) = 0 (-30 + 70x + (15x + -35x2)) = 0 Combine like terms: 70x + 15x = 85x (-30 + 85x + -35x2) = 0 Solving -30 + 85x + -35x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + 17x + -7x2) = 0 Factor a trinomial. 5((-2 + x)(3 + -7x)) = 0 Ignore the factor 5.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 '(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, 0.4285714286}
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