x^3-62x^2+61x=0

Solution for x^3-62x^2+61x=0 equation:

Simplifying
x3 + -62x2 + 61x = 0

Reorder the terms:
61x + -62x2 + x3 = 0

Solving
61x + -62x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(61 + -62x + x2) = 0

Factor a trinomial.
x((1 + -1x)(61 + -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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Subproblem 3
Set the factor '(61 + -1x)' equal to zero and attempt to solve:

Simplifying
61 + -1x = 0

Solving
61 + -1x = 0

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

Add '-61' to each side of the equation.
61 + -61 + -1x = 0 + -61

Combine like terms: 61 + -61 = 0
0 + -1x = 0 + -61
-1x = 0 + -61

Combine like terms: 0 + -61 = -61
-1x = -61

Divide each side by '-1'.
x = 61

Simplifying
x = 61
Solution
x = {0, 1, 61}