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Simplifying 4x3 + 21x2 = -5x Reorder the terms: 21x2 + 4x3 = -5x Solving 21x2 + 4x3 = -5x Solving for variable 'x'. Reorder the terms: 5x + 21x2 + 4x3 = -5x + 5x Combine like terms: -5x + 5x = 0 5x + 21x2 + 4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 21x + 4x2) = 0 Factor a trinomial. x((5 + x)(1 + 4x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {0, -5, -0.25}
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