7y(3y+5)-(4y-6)+y(2y-7)=

Solution for 7y(3y+5)-(4y-6)+y(2y-7)= equation:

Simplifying
7y(3y + 5) + -1(4y + -6) + y(2y + -7) = 0

Reorder the terms:
7y(5 + 3y) + -1(4y + -6) + y(2y + -7) = 0
(5 * 7y + 3y * 7y) + -1(4y + -6) + y(2y + -7) = 0
(35y + 21y2) + -1(4y + -6) + y(2y + -7) = 0

Reorder the terms:
35y + 21y2 + -1(-6 + 4y) + y(2y + -7) = 0
35y + 21y2 + (-6 * -1 + 4y * -1) + y(2y + -7) = 0
35y + 21y2 + (6 + -4y) + y(2y + -7) = 0

Reorder the terms:
35y + 21y2 + 6 + -4y + y(-7 + 2y) = 0
35y + 21y2 + 6 + -4y + (-7 * y + 2y * y) = 0
35y + 21y2 + 6 + -4y + (-7y + 2y2) = 0

Reorder the terms:
6 + 35y + -4y + -7y + 21y2 + 2y2 = 0

Combine like terms: 35y + -4y = 31y
6 + 31y + -7y + 21y2 + 2y2 = 0

Combine like terms: 31y + -7y = 24y
6 + 24y + 21y2 + 2y2 = 0

Combine like terms: 21y2 + 2y2 = 23y2
6 + 24y + 23y2 = 0

Solving
6 + 24y + 23y2 = 0

Solving for variable 'y'.

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

Divide each side by '23'.
0.2608695652 + 1.043478261y + y2 = 0

Move the constant term to the right:

Add '-0.2608695652' to each side of the equation.
0.2608695652 + 1.043478261y + -0.2608695652 + y2 = 0 + -0.2608695652

Reorder the terms:
0.2608695652 + -0.2608695652 + 1.043478261y + y2 = 0 + -0.2608695652

Combine like terms: 0.2608695652 + -0.2608695652 = 0.0000000000
0.0000000000 + 1.043478261y + y2 = 0 + -0.2608695652
1.043478261y + y2 = 0 + -0.2608695652

Combine like terms: 0 + -0.2608695652 = -0.2608695652
1.043478261y + y2 = -0.2608695652

The y term is 1.043478261y.  Take half its coefficient (0.5217391305).
Square it (0.2722117203) and add it to both sides.

Add '0.2722117203' to each side of the equation.
1.043478261y + 0.2722117203 + y2 = -0.2608695652 + 0.2722117203

Reorder the terms:
0.2722117203 + 1.043478261y + y2 = -0.2608695652 + 0.2722117203

Combine like terms: -0.2608695652 + 0.2722117203 = 0.0113421551
0.2722117203 + 1.043478261y + y2 = 0.0113421551

Factor a perfect square on the left side:
(y + 0.5217391305)(y + 0.5217391305) = 0.0113421551

Calculate the square root of the right side: 0.106499554

Break this problem into two subproblems by setting 
(y + 0.5217391305) equal to 0.106499554 and -0.106499554.

Subproblem 1
y + 0.5217391305 = 0.106499554

Simplifying
y + 0.5217391305 = 0.106499554

Reorder the terms:
0.5217391305 + y = 0.106499554

Solving
0.5217391305 + y = 0.106499554

Solving for variable 'y'.

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

Add '-0.5217391305' to each side of the equation.
0.5217391305 + -0.5217391305 + y = 0.106499554 + -0.5217391305

Combine like terms: 0.5217391305 + -0.5217391305 = 0.0000000000
0.0000000000 + y = 0.106499554 + -0.5217391305
y = 0.106499554 + -0.5217391305

Combine like terms: 0.106499554 + -0.5217391305 = -0.4152395765
y = -0.4152395765

Simplifying
y = -0.4152395765

Subproblem 2
y + 0.5217391305 = -0.106499554

Simplifying
y + 0.5217391305 = -0.106499554

Reorder the terms:
0.5217391305 + y = -0.106499554

Solving
0.5217391305 + y = -0.106499554

Solving for variable 'y'.

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

Add '-0.5217391305' to each side of the equation.
0.5217391305 + -0.5217391305 + y = -0.106499554 + -0.5217391305

Combine like terms: 0.5217391305 + -0.5217391305 = 0.0000000000
0.0000000000 + y = -0.106499554 + -0.5217391305
y = -0.106499554 + -0.5217391305

Combine like terms: -0.106499554 + -0.5217391305 = -0.6282386845
y = -0.6282386845

Simplifying
y = -0.6282386845

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.4152395765, -0.6282386845}