4x^3-9x^2+6x=0

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Solution for 4x^3-9x^2+6x=0 equation:


Simplifying
4x3 + -9x2 + 6x = 0

Reorder the terms:
6x + -9x2 + 4x3 = 0

Solving
6x + -9x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + -9x + 4x2) = 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 '(6 + -9x + 4x2)' equal to zero and attempt to solve: Simplifying 6 + -9x + 4x2 = 0 Solving 6 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.5 + -2.25x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2.25x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2.25x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2.25x + x2 = 0 + -1.5 -2.25x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2.25x + x2 = -1.5 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = -1.5 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = -1.5 + 1.265625 Combine like terms: -1.5 + 1.265625 = -0.234375 1.265625 + -2.25x + x2 = -0.234375 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = -0.234375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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