y(2y-19)=33

Solution for y(2y-19)=33 equation:

Simplifying
y(2y + -19) = 33

Reorder the terms:
y(-19 + 2y) = 33
(-19 * y + 2y * y) = 33
(-19y + 2y2) = 33

Solving
-19y + 2y2 = 33

Solving for variable 'y'.

Reorder the terms:
-33 + -19y + 2y2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + -19y + 2y2 = 0

Factor a trinomial.
(-3 + -2y)(11 + -1y) = 0

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

Simplifying
-3 + -2y = 0

Solving
-3 + -2y = 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 + -2y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2y = 0 + 3
-2y = 0 + 3

Combine like terms: 0 + 3 = 3
-2y = 3

Divide each side by '-2'.
y = -1.5

Simplifying
y = -1.5
Subproblem 2
Set the factor '(11 + -1y)' equal to zero and attempt to solve:

Simplifying
11 + -1y = 0

Solving
11 + -1y = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1y = 0 + -11
-1y = 0 + -11

Combine like terms: 0 + -11 = -11
-1y = -11

Divide each side by '-1'.
y = 11

Simplifying
y = 11
Solution
y = {-1.5, 11}