5y=4y^2-6

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

Simplifying
5y = 4y2 + -6

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

Solving
5y = -6 + 4y2

Solving for variable 'y'.

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

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

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

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

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

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

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

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

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

Divide each side by '-1'.
y = 2

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

Simplifying
3 + 4y = 0

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

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

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

Divide each side by '4'.
y = -0.75

Simplifying
y = -0.75
Solution
y = {2, -0.75}