25x^3-15x^2+60x=0

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Solution for 25x^3-15x^2+60x=0 equation:


Simplifying
25x3 + -15x2 + 60x = 0

Reorder the terms:
60x + -15x2 + 25x3 = 0

Solving
60x + -15x2 + 25x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(12 + -3x + 5x2) = 0

Ignore the factor 5.

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 '(12 + -3x + 5x2)' equal to zero and attempt to solve: Simplifying 12 + -3x + 5x2 = 0 Solving 12 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + -0.6x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -0.6x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -0.6x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -0.6x + x2 = 0 + -2.4 -0.6x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -0.6x + x2 = -2.4 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = -2.4 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = -2.4 + 0.09 Combine like terms: -2.4 + 0.09 = -2.31 0.09 + -0.6x + x2 = -2.31 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = -2.31 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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