6y^2=5y+4

Solution for 6y^2=5y+4 equation:

Simplifying
6y2 = 5y + 4

Reorder the terms:
6y2 = 4 + 5y

Solving
6y2 = 4 + 5y

Solving for variable 'y'.

Reorder the terms:
-4 + -5y + 6y2 = 4 + 5y + -4 + -5y

Reorder the terms:
-4 + -5y + 6y2 = 4 + -4 + 5y + -5y

Combine like terms: 4 + -4 = 0
-4 + -5y + 6y2 = 0 + 5y + -5y
-4 + -5y + 6y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-4 + -5y + 6y2 = 0

Factor a trinomial.
(-1 + -2y)(4 + -3y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -3y)' equal to zero and attempt to solve:

Simplifying
4 + -3y = 0

Solving
4 + -3y = 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 + -3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3y = 0 + -4
-3y = 0 + -4

Combine like terms: 0 + -4 = -4
-3y = -4

Divide each side by '-3'.
y = 1.333333333

Simplifying
y = 1.333333333
Solution
y = {-0.5, 1.333333333}