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Simplifying 0 = 15x4 + 60x3 + -75x2 Reorder the terms: 0 = -75x2 + 60x3 + 15x4 Solving 0 = -75x2 + 60x3 + 15x4 Solving for variable 'x'. Remove the zero: 75x2 + -60x3 + -15x4 = -75x2 + 60x3 + 15x4 + 75x2 + -60x3 + -15x4 Reorder the terms: 75x2 + -60x3 + -15x4 = -75x2 + 75x2 + 60x3 + -60x3 + 15x4 + -15x4 Combine like terms: -75x2 + 75x2 = 0 75x2 + -60x3 + -15x4 = 0 + 60x3 + -60x3 + 15x4 + -15x4 75x2 + -60x3 + -15x4 = 60x3 + -60x3 + 15x4 + -15x4 Combine like terms: 60x3 + -60x3 = 0 75x2 + -60x3 + -15x4 = 0 + 15x4 + -15x4 75x2 + -60x3 + -15x4 = 15x4 + -15x4 Combine like terms: 15x4 + -15x4 = 0 75x2 + -60x3 + -15x4 = 0 Factor out the Greatest Common Factor (GCF), '15x2'. 15x2(5 + -4x + -1x2) = 0 Factor a trinomial. 15x2((1 + -1x)(5 + x)) = 0 Ignore the factor 15.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
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 3
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {0, 1, -5}
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