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Simplifying (3 + -1x)(4x2 + -1x + 0) = 0 Reorder the terms: (3 + -1x)(0 + -1x + 4x2) = 0 Remove the zero: (3 + -1x)(-1x + 4x2) = 0 Multiply (3 + -1x) * (-1x + 4x2) (3(-1x + 4x2) + -1x * (-1x + 4x2)) = 0 ((-1x * 3 + 4x2 * 3) + -1x * (-1x + 4x2)) = 0 ((-3x + 12x2) + -1x * (-1x + 4x2)) = 0 (-3x + 12x2 + (-1x * -1x + 4x2 * -1x)) = 0 (-3x + 12x2 + (1x2 + -4x3)) = 0 Combine like terms: 12x2 + 1x2 = 13x2 (-3x + 13x2 + -4x3) = 0 Solving -3x + 13x2 + -4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + 13x + -4x2) = 0 Factor a trinomial. x((-3 + 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 '(-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 = 3Subproblem 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, 3, 0.25}
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