-7y(-63y+18)=63y+18

Solution for -7y(-63y+18)=63y+18 equation:

Simplifying
-7y(-63y + 18) = 63y + 18

Reorder the terms:
-7y(18 + -63y) = 63y + 18
(18 * -7y + -63y * -7y) = 63y + 18
(-126y + 441y2) = 63y + 18

Reorder the terms:
-126y + 441y2 = 18 + 63y

Solving
-126y + 441y2 = 18 + 63y

Solving for variable 'y'.

Reorder the terms:
-18 + -126y + -63y + 441y2 = 18 + 63y + -18 + -63y

Combine like terms: -126y + -63y = -189y
-18 + -189y + 441y2 = 18 + 63y + -18 + -63y

Reorder the terms:
-18 + -189y + 441y2 = 18 + -18 + 63y + -63y

Combine like terms: 18 + -18 = 0
-18 + -189y + 441y2 = 0 + 63y + -63y
-18 + -189y + 441y2 = 63y + -63y

Combine like terms: 63y + -63y = 0
-18 + -189y + 441y2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-2 + -21y + 49y2) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-2 + -21y + 49y2)' equal to zero and attempt to solve:

Simplifying
-2 + -21y + 49y2 = 0

Solving
-2 + -21y + 49y2 = 0

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

Divide each side by '49'.
-0.04081632653 + -0.4285714286y + y2 = 0

Move the constant term to the right:

Add '0.04081632653' to each side of the equation.
-0.04081632653 + -0.4285714286y + 0.04081632653 + y2 = 0 + 0.04081632653

Reorder the terms:
-0.04081632653 + 0.04081632653 + -0.4285714286y + y2 = 0 + 0.04081632653

Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000
0.00000000000 + -0.4285714286y + y2 = 0 + 0.04081632653
-0.4285714286y + y2 = 0 + 0.04081632653

Combine like terms: 0 + 0.04081632653 = 0.04081632653
-0.4285714286y + y2 = 0.04081632653

The y term is -0.4285714286y.  Take half its coefficient (-0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
-0.4285714286y + 0.04591836735 + y2 = 0.04081632653 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286y + y2 = 0.04081632653 + 0.04591836735

Combine like terms: 0.04081632653 + 0.04591836735 = 0.08673469388
0.04591836735 + -0.4285714286y + y2 = 0.08673469388

Factor a perfect square on the left side:
(y + -0.2142857143)(y + -0.2142857143) = 0.08673469388

Calculate the square root of the right side: 0.294507545

Break this problem into two subproblems by setting 
(y + -0.2142857143) equal to 0.294507545 and -0.294507545.

Subproblem 1
y + -0.2142857143 = 0.294507545

Simplifying
y + -0.2142857143 = 0.294507545

Reorder the terms:
-0.2142857143 + y = 0.294507545

Solving
-0.2142857143 + y = 0.294507545

Solving for variable 'y'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + y = 0.294507545 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + y = 0.294507545 + 0.2142857143
y = 0.294507545 + 0.2142857143

Combine like terms: 0.294507545 + 0.2142857143 = 0.5087932593
y = 0.5087932593

Simplifying
y = 0.5087932593

Subproblem 2
y + -0.2142857143 = -0.294507545

Simplifying
y + -0.2142857143 = -0.294507545

Reorder the terms:
-0.2142857143 + y = -0.294507545

Solving
-0.2142857143 + y = -0.294507545

Solving for variable 'y'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + y = -0.294507545 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + y = -0.294507545 + 0.2142857143
y = -0.294507545 + 0.2142857143

Combine like terms: -0.294507545 + 0.2142857143 = -0.0802218307
y = -0.0802218307

Simplifying
y = -0.0802218307

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.5087932593, -0.0802218307}
Solution
y = {0.5087932593, -0.0802218307}