2x^3=14x^2-60x

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Solution for 2x^3=14x^2-60x equation: 


Simplifying
2x3 = 14x2 + -60x

Reorder the terms:
2x3 = -60x + 14x2

Solving
2x3 = -60x + 14x2

Solving for variable 'x'.

Reorder the terms:
60x + -14x2 + 2x3 = -60x + 14x2 + 60x + -14x2

Reorder the terms:
60x + -14x2 + 2x3 = -60x + 60x + 14x2 + -14x2

Combine like terms: -60x + 60x = 0
60x + -14x2 + 2x3 = 0 + 14x2 + -14x2
60x + -14x2 + 2x3 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
60x + -14x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(30 + -7x + x2) = 0

Ignore the factor 2.

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 '(30 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
30 + -7x + x2 = 0

Solving
30 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -7x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + -7x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -7x + x2 = 0 + -30
-7x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
-7x + x2 = -30

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -30 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -30 + 12.25

Combine like terms: -30 + 12.25 = -17.75
12.25 + -7x + x2 = -17.75

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = -17.75

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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