5-(2y-3)y=6

Solution for 5-(2y-3)y=6 equation:

Simplifying
5 + -1(2y + -3) * y = 6

Reorder the terms:
5 + -1(-3 + 2y) * y = 6

Reorder the terms for easier multiplication:
5 + -1y(-3 + 2y) = 6
5 + (-3 * -1y + 2y * -1y) = 6
5 + (3y + -2y2) = 6

Solving
5 + 3y + -2y2 = 6

Solving for variable 'y'.

Reorder the terms:
5 + -6 + 3y + -2y2 = 6 + -6

Combine like terms: 5 + -6 = -1
-1 + 3y + -2y2 = 6 + -6

Combine like terms: 6 + -6 = 0
-1 + 3y + -2y2 = 0

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

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

Simplifying
-1 + y = 0

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

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

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

Simplifying
y = 1
Subproblem 2
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
Solution
y = {1, 0.5}