y(2y-6)+3=11

Solution for y(2y-6)+3=11 equation:

Simplifying
y(2y + -6) + 3 = 11

Reorder the terms:
y(-6 + 2y) + 3 = 11
(-6 * y + 2y * y) + 3 = 11
(-6y + 2y2) + 3 = 11

Reorder the terms:
3 + -6y + 2y2 = 11

Solving
3 + -6y + 2y2 = 11

Solving for variable 'y'.

Reorder the terms:
3 + -11 + -6y + 2y2 = 11 + -11

Combine like terms: 3 + -11 = -8
-8 + -6y + 2y2 = 11 + -11

Combine like terms: 11 + -11 = 0
-8 + -6y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -3y + y2) = 0

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

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

Simplifying
-1 + -1y = 0

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

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

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

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

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

Simplifying
4 + -1y = 0

Solving
4 + -1y = 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 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-1, 4}