7y^4-18y^3-9y^2=0

Solution for 7y^4-18y^3-9y^2=0 equation:

Simplifying
7y4 + -18y3 + -9y2 = 0

Reorder the terms:
-9y2 + -18y3 + 7y4 = 0

Solving
-9y2 + -18y3 + 7y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(-9 + -18y + 7y2) = 0

Factor a trinomial.
y2((-3 + -7y)(3 + -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 '(-3 + -7y)' equal to zero and attempt to solve:

Simplifying
-3 + -7y = 0

Solving
-3 + -7y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -7y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7y = 0 + 3
-7y = 0 + 3

Combine like terms: 0 + 3 = 3
-7y = 3

Divide each side by '-7'.
y = -0.4285714286

Simplifying
y = -0.4285714286
Subproblem 3
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

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

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

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {0, -0.4285714286, 3}