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Simplifying 0 = -3x4 + -24x3 + -45x2 Reorder the terms: 0 = -45x2 + -24x3 + -3x4 Solving 0 = -45x2 + -24x3 + -3x4 Solving for variable 'x'. Remove the zero: 45x2 + 24x3 + 3x4 = -45x2 + -24x3 + -3x4 + 45x2 + 24x3 + 3x4 Reorder the terms: 45x2 + 24x3 + 3x4 = -45x2 + 45x2 + -24x3 + 24x3 + -3x4 + 3x4 Combine like terms: -45x2 + 45x2 = 0 45x2 + 24x3 + 3x4 = 0 + -24x3 + 24x3 + -3x4 + 3x4 45x2 + 24x3 + 3x4 = -24x3 + 24x3 + -3x4 + 3x4 Combine like terms: -24x3 + 24x3 = 0 45x2 + 24x3 + 3x4 = 0 + -3x4 + 3x4 45x2 + 24x3 + 3x4 = -3x4 + 3x4 Combine like terms: -3x4 + 3x4 = 0 45x2 + 24x3 + 3x4 = 0 Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(15 + 8x + x2) = 0 Factor a trinomial. 3x2((5 + x)(3 + x)) = 0 Ignore the factor 3.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 '(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 = -5Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {0, -5, -3}
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