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Simplifying 5x4 + -16x3 + -21x2 = 0 Reorder the terms: -21x2 + -16x3 + 5x4 = 0 Solving -21x2 + -16x3 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-21 + -16x + 5x2) = 0 Factor a trinomial. x2((-1 + -1x)(21 + -5x)) = 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 '(-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 '(21 + -5x)' equal to zero and attempt to solve: Simplifying 21 + -5x = 0 Solving 21 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -5x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -5x = 0 + -21 -5x = 0 + -21 Combine like terms: 0 + -21 = -21 -5x = -21 Divide each side by '-5'. x = 4.2 Simplifying x = 4.2Solution
x = {0, -1, 4.2}
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