3x^3-14x^2=5x

Solution for 3x^3-14x^2=5x equation:

Simplifying
3x3 + -14x2 = 5x

Reorder the terms:
-14x2 + 3x3 = 5x

Solving
-14x2 + 3x3 = 5x

Solving for variable 'x'.

Reorder the terms:
-5x + -14x2 + 3x3 = 5x + -5x

Combine like terms: 5x + -5x = 0
-5x + -14x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + -14x + 3x2) = 0

Factor a trinomial.
x((-1 + -3x)(5 + -1x)) = 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 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, -0.3333333333, 5}