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Simplifying 0 = 15x4 + -75x2 + 60 Reorder the terms: 0 = 60 + -75x2 + 15x4 Solving 0 = 60 + -75x2 + 15x4 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + 75x2 + -15x4 = 60 + -75x2 + 15x4 + -60 + 75x2 + -15x4 Reorder the terms: -60 + 75x2 + -15x4 = 60 + -60 + -75x2 + 75x2 + 15x4 + -15x4 Combine like terms: 60 + -60 = 0 -60 + 75x2 + -15x4 = 0 + -75x2 + 75x2 + 15x4 + -15x4 -60 + 75x2 + -15x4 = -75x2 + 75x2 + 15x4 + -15x4 Combine like terms: -75x2 + 75x2 = 0 -60 + 75x2 + -15x4 = 0 + 15x4 + -15x4 -60 + 75x2 + -15x4 = 15x4 + -15x4 Combine like terms: 15x4 + -15x4 = 0 -60 + 75x2 + -15x4 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-4 + 5x2 + -1x4) = 0 Factor a trinomial. 15((-4 + x2)(1 + -1x2)) = 0 Factor a difference between two squares. 15(((2 + x)(-2 + x))(1 + -1x2)) = 0 Factor a difference between two squares. 15(((1 + x)(1 + -1x))(2 + x)(-2 + x)) = 0 Ignore the factor 15.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 '(-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 3
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 4
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 = 1Solution
x = {-2, 2, -1, 1}
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