7y(9y-16)=14-(-y+19)

Solution for 7y(9y-16)=14-(-y+19) equation:

Simplifying
7y(9y + -16) = 14 + -1(-1y + 19)

Reorder the terms:
7y(-16 + 9y) = 14 + -1(-1y + 19)
(-16 * 7y + 9y * 7y) = 14 + -1(-1y + 19)
(-112y + 63y2) = 14 + -1(-1y + 19)

Reorder the terms:
-112y + 63y2 = 14 + -1(19 + -1y)
-112y + 63y2 = 14 + (19 * -1 + -1y * -1)
-112y + 63y2 = 14 + (-19 + 1y)

Combine like terms: 14 + -19 = -5
-112y + 63y2 = -5 + 1y

Solving
-112y + 63y2 = -5 + 1y

Solving for variable 'y'.

Reorder the terms:
5 + -112y + -1y + 63y2 = -5 + 1y + 5 + -1y

Combine like terms: -112y + -1y = -113y
5 + -113y + 63y2 = -5 + 1y + 5 + -1y

Reorder the terms:
5 + -113y + 63y2 = -5 + 5 + 1y + -1y

Combine like terms: -5 + 5 = 0
5 + -113y + 63y2 = 0 + 1y + -1y
5 + -113y + 63y2 = 1y + -1y

Combine like terms: 1y + -1y = 0
5 + -113y + 63y2 = 0

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

Divide each side by '63'.
0.07936507937 + -1.793650794y + y2 = 0

Move the constant term to the right:

Add '-0.07936507937' to each side of the equation.
0.07936507937 + -1.793650794y + -0.07936507937 + y2 = 0 + -0.07936507937

Reorder the terms:
0.07936507937 + -0.07936507937 + -1.793650794y + y2 = 0 + -0.07936507937

Combine like terms: 0.07936507937 + -0.07936507937 = 0.00000000000
0.00000000000 + -1.793650794y + y2 = 0 + -0.07936507937
-1.793650794y + y2 = 0 + -0.07936507937

Combine like terms: 0 + -0.07936507937 = -0.07936507937
-1.793650794y + y2 = -0.07936507937

The y term is -1.793650794y.  Take half its coefficient (-0.896825397).
Square it (0.8042957927) and add it to both sides.

Add '0.8042957927' to each side of the equation.
-1.793650794y + 0.8042957927 + y2 = -0.07936507937 + 0.8042957927

Reorder the terms:
0.8042957927 + -1.793650794y + y2 = -0.07936507937 + 0.8042957927

Combine like terms: -0.07936507937 + 0.8042957927 = 0.72493071333
0.8042957927 + -1.793650794y + y2 = 0.72493071333

Factor a perfect square on the left side:
(y + -0.896825397)(y + -0.896825397) = 0.72493071333

Calculate the square root of the right side: 0.851428631

Break this problem into two subproblems by setting 
(y + -0.896825397) equal to 0.851428631 and -0.851428631.

Subproblem 1
y + -0.896825397 = 0.851428631

Simplifying
y + -0.896825397 = 0.851428631

Reorder the terms:
-0.896825397 + y = 0.851428631

Solving
-0.896825397 + y = 0.851428631

Solving for variable 'y'.

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

Add '0.896825397' to each side of the equation.
-0.896825397 + 0.896825397 + y = 0.851428631 + 0.896825397

Combine like terms: -0.896825397 + 0.896825397 = 0.000000000
0.000000000 + y = 0.851428631 + 0.896825397
y = 0.851428631 + 0.896825397

Combine like terms: 0.851428631 + 0.896825397 = 1.748254028
y = 1.748254028

Simplifying
y = 1.748254028

Subproblem 2
y + -0.896825397 = -0.851428631

Simplifying
y + -0.896825397 = -0.851428631

Reorder the terms:
-0.896825397 + y = -0.851428631

Solving
-0.896825397 + y = -0.851428631

Solving for variable 'y'.

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

Add '0.896825397' to each side of the equation.
-0.896825397 + 0.896825397 + y = -0.851428631 + 0.896825397

Combine like terms: -0.896825397 + 0.896825397 = 0.000000000
0.000000000 + y = -0.851428631 + 0.896825397
y = -0.851428631 + 0.896825397

Combine like terms: -0.851428631 + 0.896825397 = 0.045396766
y = 0.045396766

Simplifying
y = 0.045396766

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.748254028, 0.045396766}