3x^3-(9x^2)=-27x

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Solution for 3x^3-(9x^2)=-27x equation: 


Simplifying
3x3 + -1(9x2) = -27x

Remove parenthesis around (9x2)
3x3 + -1 * 9x2 = -27x

Multiply -1 * 9
3x3 + -9x2 = -27x

Reorder the terms:
-9x2 + 3x3 = -27x

Solving
-9x2 + 3x3 = -27x

Solving for variable 'x'.

Reorder the terms:
27x + -9x2 + 3x3 = -27x + 27x

Combine like terms: -27x + 27x = 0
27x + -9x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(9 + -3x + x2) = 0

Ignore the factor 3.

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 '(9 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
9 + -3x + x2 = 0

Solving
9 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -3x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -3x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -3x + x2 = 0 + -9
-3x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-3x + x2 = -9

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -9 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -9 + 2.25

Combine like terms: -9 + 2.25 = -6.75
2.25 + -3x + x2 = -6.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -6.75

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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