2y^2-5y=21-6y

Solution for 2y^2-5y=21-6y equation:

Simplifying
2y2 + -5y = 21 + -6y

Reorder the terms:
-5y + 2y2 = 21 + -6y

Solving
-5y + 2y2 = 21 + -6y

Solving for variable 'y'.

Reorder the terms:
-21 + -5y + 6y + 2y2 = 21 + -6y + -21 + 6y

Combine like terms: -5y + 6y = 1y
-21 + 1y + 2y2 = 21 + -6y + -21 + 6y

Reorder the terms:
-21 + 1y + 2y2 = 21 + -21 + -6y + 6y

Combine like terms: 21 + -21 = 0
-21 + 1y + 2y2 = 0 + -6y + 6y
-21 + 1y + 2y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
-21 + 1y + 2y2 = 0

Factor a trinomial.
(-7 + -2y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-7 + -2y)' equal to zero and attempt to solve:

Simplifying
-7 + -2y = 0

Solving
-7 + -2y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2y = 0 + 7
-2y = 0 + 7

Combine like terms: 0 + 7 = 7
-2y = 7

Divide each side by '-2'.
y = -3.5

Simplifying
y = -3.5
Subproblem 2
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 = {-3.5, 3}