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Simplifying (15x + 15)(-1 + 16x) = 0 Reorder the terms: (15 + 15x)(-1 + 16x) = 0 Multiply (15 + 15x) * (-1 + 16x) (15(-1 + 16x) + 15x * (-1 + 16x)) = 0 ((-1 * 15 + 16x * 15) + 15x * (-1 + 16x)) = 0 ((-15 + 240x) + 15x * (-1 + 16x)) = 0 (-15 + 240x + (-1 * 15x + 16x * 15x)) = 0 (-15 + 240x + (-15x + 240x2)) = 0 Combine like terms: 240x + -15x = 225x (-15 + 225x + 240x2) = 0 Solving -15 + 225x + 240x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '15'. 15(-1 + 15x + 16x2) = 0 Factor a trinomial. 15((-1 + -1x)(1 + -16x)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + -16x)' equal to zero and attempt to solve: Simplifying 1 + -16x = 0 Solving 1 + -16x = 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 + -16x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -16x = 0 + -1 -16x = 0 + -1 Combine like terms: 0 + -1 = -1 -16x = -1 Divide each side by '-16'. x = 0.0625 Simplifying x = 0.0625Solution
x = {-1, 0.0625}
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