y^2+3y=7y

Solution for y^2+3y=7y equation:

Simplifying
y2 + 3y = 7y

Reorder the terms:
3y + y2 = 7y

Solving
3y + y2 = 7y

Solving for variable 'y'.

Reorder the terms:
3y + -7y + y2 = 7y + -7y

Combine like terms: 3y + -7y = -4y
-4y + y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
-4y + y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-4 + y) = 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 '(-4 + y)' equal to zero and attempt to solve:

Simplifying
-4 + y = 0

Solving
-4 + y = 0

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

Add '4' to each side of the equation.
-4 + 4 + y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + y = 0 + 4
y = 0 + 4

Combine like terms: 0 + 4 = 4
y = 4

Simplifying
y = 4
Solution
y = {0, 4}