4y^4=32y^3-68y^2

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Solution for 4y^4=32y^3-68y^2 equation: 


Simplifying
4y4 = 32y3 + -68y2

Reorder the terms:
4y4 = -68y2 + 32y3

Solving
4y4 = -68y2 + 32y3

Solving for variable 'y'.

Reorder the terms:
68y2 + -32y3 + 4y4 = -68y2 + 32y3 + 68y2 + -32y3

Reorder the terms:
68y2 + -32y3 + 4y4 = -68y2 + 68y2 + 32y3 + -32y3

Combine like terms: -68y2 + 68y2 = 0
68y2 + -32y3 + 4y4 = 0 + 32y3 + -32y3
68y2 + -32y3 + 4y4 = 32y3 + -32y3

Combine like terms: 32y3 + -32y3 = 0
68y2 + -32y3 + 4y4 = 0

Factor out the Greatest Common Factor (GCF), '4y2'.
4y2(17 + -8y + y2) = 0

Ignore the factor 4.

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 '(17 + -8y + y2)' equal to zero and attempt to solve:

Simplifying
17 + -8y + y2 = 0

Solving
17 + -8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -8y + -17 + y2 = 0 + -17

Reorder the terms:
17 + -17 + -8y + y2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -8y + y2 = 0 + -17
-8y + y2 = 0 + -17

Combine like terms: 0 + -17 = -17
-8y + y2 = -17

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = -17 + 16

Reorder the terms:
16 + -8y + y2 = -17 + 16

Combine like terms: -17 + 16 = -1
16 + -8y + y2 = -1

Factor a perfect square on the left side:
(y + -4)(y + -4) = -1

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
y = {0}

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