-4x^3+x=3x^2

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Solution for -4x^3+x=3x^2 equation:


Simplifying
-4x3 + x = 3x2

Reorder the terms:
x + -4x3 = 3x2

Solving
x + -4x3 = 3x2

Solving for variable 'x'.

Reorder the terms:
x + -3x2 + -4x3 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
x + -3x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -3x + -4x2) = 0

Factor a trinomial.
x((1 + -4x)(1 + x)) = 0

Subproblem 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 = 0

Subproblem 2

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 = 0.25

Subproblem 3

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {0, 0.25, -1}

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