2y(4y-1)=18

Solution for 2y(4y-1)=18 equation:

Simplifying
2y(4y + -1) = 18

Reorder the terms:
2y(-1 + 4y) = 18
(-1 * 2y + 4y * 2y) = 18
(-2y + 8y2) = 18

Solving
-2y + 8y2 = 18

Solving for variable 'y'.

Reorder the terms:
-18 + -2y + 8y2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -2y + 8y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -1y + 4y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -1y + 4y2)' equal to zero and attempt to solve:

Simplifying
-9 + -1y + 4y2 = 0

Solving
-9 + -1y + 4y2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-2.25 + -0.25y + y2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -0.25y + 2.25 + y2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -0.25y + y2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -0.25y + y2 = 0 + 2.25
-0.25y + y2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-0.25y + y2 = 2.25

The y term is -0.25y.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25y + 0.015625 + y2 = 2.25 + 0.015625

Reorder the terms:
0.015625 + -0.25y + y2 = 2.25 + 0.015625

Combine like terms: 2.25 + 0.015625 = 2.265625
0.015625 + -0.25y + y2 = 2.265625

Factor a perfect square on the left side:
(y + -0.125)(y + -0.125) = 2.265625

Calculate the square root of the right side: 1.505199322

Break this problem into two subproblems by setting 
(y + -0.125) equal to 1.505199322 and -1.505199322.

Subproblem 1
y + -0.125 = 1.505199322

Simplifying
y + -0.125 = 1.505199322

Reorder the terms:
-0.125 + y = 1.505199322

Solving
-0.125 + y = 1.505199322

Solving for variable 'y'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + y = 1.505199322 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + y = 1.505199322 + 0.125
y = 1.505199322 + 0.125

Combine like terms: 1.505199322 + 0.125 = 1.630199322
y = 1.630199322

Simplifying
y = 1.630199322

Subproblem 2
y + -0.125 = -1.505199322

Simplifying
y + -0.125 = -1.505199322

Reorder the terms:
-0.125 + y = -1.505199322

Solving
-0.125 + y = -1.505199322

Solving for variable 'y'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + y = -1.505199322 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + y = -1.505199322 + 0.125
y = -1.505199322 + 0.125

Combine like terms: -1.505199322 + 0.125 = -1.380199322
y = -1.380199322

Simplifying
y = -1.380199322

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.630199322, -1.380199322}
Solution
y = {1.630199322, -1.380199322}