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Simplifying 0 = 4x3 + 3x2 + -10x Reorder the terms: 0 = -10x + 3x2 + 4x3 Solving 0 = -10x + 3x2 + 4x3 Solving for variable 'x'. Remove the zero: 10x + -3x2 + -4x3 = -10x + 3x2 + 4x3 + 10x + -3x2 + -4x3 Reorder the terms: 10x + -3x2 + -4x3 = -10x + 10x + 3x2 + -3x2 + 4x3 + -4x3 Combine like terms: -10x + 10x = 0 10x + -3x2 + -4x3 = 0 + 3x2 + -3x2 + 4x3 + -4x3 10x + -3x2 + -4x3 = 3x2 + -3x2 + 4x3 + -4x3 Combine like terms: 3x2 + -3x2 = 0 10x + -3x2 + -4x3 = 0 + 4x3 + -4x3 10x + -3x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 10x + -3x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(10 + -3x + -4x2) = 0 Factor a trinomial. x((5 + -4x)(2 + x)) = 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 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {0, 1.25, -2}
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