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Simplifying 0 = 4x4 + -12x3 + 5x2 Reorder the terms: 0 = 5x2 + -12x3 + 4x4 Solving 0 = 5x2 + -12x3 + 4x4 Solving for variable 'x'. Remove the zero: -5x2 + 12x3 + -4x4 = 5x2 + -12x3 + 4x4 + -5x2 + 12x3 + -4x4 Reorder the terms: -5x2 + 12x3 + -4x4 = 5x2 + -5x2 + -12x3 + 12x3 + 4x4 + -4x4 Combine like terms: 5x2 + -5x2 = 0 -5x2 + 12x3 + -4x4 = 0 + -12x3 + 12x3 + 4x4 + -4x4 -5x2 + 12x3 + -4x4 = -12x3 + 12x3 + 4x4 + -4x4 Combine like terms: -12x3 + 12x3 = 0 -5x2 + 12x3 + -4x4 = 0 + 4x4 + -4x4 -5x2 + 12x3 + -4x4 = 4x4 + -4x4 Combine like terms: 4x4 + -4x4 = 0 -5x2 + 12x3 + -4x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-5 + 12x + -4x2) = 0 Factor a trinomial. x2((-5 + 2x)(1 + -2x)) = 0Subproblem 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 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 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 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Divide each side by '2'. x = 2.5 Simplifying x = 2.5Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {0, 2.5, 0.5}
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