y^4-13y^3=-42y^2

Solution for y^4-13y^3=-42y^2 equation:

Simplifying
y4 + -13y3 = -42y2

Reorder the terms:
-13y3 + y4 = -42y2

Solving
-13y3 + y4 = -42y2

Solving for variable 'y'.

Reorder the terms:
42y2 + -13y3 + y4 = -42y2 + 42y2

Combine like terms: -42y2 + 42y2 = 0
42y2 + -13y3 + y4 = 0

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(42 + -13y + y2) = 0

Factor a trinomial.
y2((6 + -1y)(7 + -1y)) = 0

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}
Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Subproblem 3
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {0, 6, 7}