2y^2+7y=8y

Solution for 2y^2+7y=8y equation:

Simplifying
2y2 + 7y = 8y

Reorder the terms:
7y + 2y2 = 8y

Solving
7y + 2y2 = 8y

Solving for variable 'y'.

Reorder the terms:
7y + -8y + 2y2 = 8y + -8y

Combine like terms: 7y + -8y = -1y
-1y + 2y2 = 8y + -8y

Combine like terms: 8y + -8y = 0
-1y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1 + 2y) = 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 '(-1 + 2y)' equal to zero and attempt to solve:

Simplifying
-1 + 2y = 0

Solving
-1 + 2y = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2y = 0 + 1
2y = 0 + 1

Combine like terms: 0 + 1 = 1
2y = 1

Divide each side by '2'.
y = 0.5

Simplifying
y = 0.5
Solution
y = {0, 0.5}