7y^2-2y^2=44y+7y

Solution for 7y^2-2y^2=44y+7y equation:

Simplifying
7y2 + -2y2 = 44y + 7y

Combine like terms: 7y2 + -2y2 = 5y2
5y2 = 44y + 7y

Combine like terms: 44y + 7y = 51y
5y2 = 51y

Solving
5y2 = 51y

Solving for variable 'y'.

Reorder the terms:
-51y + 5y2 = 51y + -51y

Combine like terms: 51y + -51y = 0
-51y + 5y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-51 + 5y) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-51 + 5y)' equal to zero and attempt to solve:

Simplifying
-51 + 5y = 0

Solving
-51 + 5y = 0

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

Add '51' to each side of the equation.
-51 + 51 + 5y = 0 + 51

Combine like terms: -51 + 51 = 0
0 + 5y = 0 + 51
5y = 0 + 51

Combine like terms: 0 + 51 = 51
5y = 51

Divide each side by '5'.
y = 10.2

Simplifying
y = 10.2
Solution
y = {0, 10.2}