6y^2-13y+5=10

Solution for 6y^2-13y+5=10 equation:

Simplifying
6y2 + -13y + 5 = 10

Reorder the terms:
5 + -13y + 6y2 = 10

Solving
5 + -13y + 6y2 = 10

Solving for variable 'y'.

Reorder the terms:
5 + -10 + -13y + 6y2 = 10 + -10

Combine like terms: 5 + -10 = -5
-5 + -13y + 6y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-5 + -13y + 6y2 = 0

Factor a trinomial.
(-1 + -3y)(5 + -2y) = 0

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

Simplifying
-1 + -3y = 0

Solving
-1 + -3y = 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 + -3y = 0 + 1

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

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

Divide each side by '-3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
Subproblem 2
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {-0.3333333333, 2.5}