(14y-5)(6)-(3y+5)(3y)=

Solution for (14y-5)(6)-(3y+5)(3y)= equation:

Simplifying
(14y + -5)(6) + -1(3y + 5)(3y) = 0

Reorder the terms:
(-5 + 14y)(6) + -1(3y + 5)(3y) = 0

Reorder the terms for easier multiplication:
6(-5 + 14y) + -1(3y + 5)(3y) = 0
(-5 * 6 + 14y * 6) + -1(3y + 5)(3y) = 0
(-30 + 84y) + -1(3y + 5)(3y) = 0

Reorder the terms:
-30 + 84y + -1(5 + 3y)(3y) = 0

Remove parenthesis around (3y)
-30 + 84y + -1(5 + 3y) * 3y = 0

Reorder the terms for easier multiplication:
-30 + 84y + -1 * 3y(5 + 3y) = 0

Multiply -1 * 3
-30 + 84y + -3y(5 + 3y) = 0
-30 + 84y + (5 * -3y + 3y * -3y) = 0
-30 + 84y + (-15y + -9y2) = 0

Combine like terms: 84y + -15y = 69y
-30 + 69y + -9y2 = 0

Solving
-30 + 69y + -9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 23y + -3y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + 23y + -3y2)' equal to zero and attempt to solve:

Simplifying
-10 + 23y + -3y2 = 0

Solving
-10 + 23y + -3y2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
3.333333333 + -7.666666667y + y2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -7.666666667y + -3.333333333 + y2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -7.666666667y + y2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -7.666666667y + y2 = 0 + -3.333333333
-7.666666667y + y2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-7.666666667y + y2 = -3.333333333

The y term is -7.666666667y.  Take half its coefficient (-3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
-7.666666667y + 14.69444445 + y2 = -3.333333333 + 14.69444445

Reorder the terms:
14.69444445 + -7.666666667y + y2 = -3.333333333 + 14.69444445

Combine like terms: -3.333333333 + 14.69444445 = 11.361111117
14.69444445 + -7.666666667y + y2 = 11.361111117

Factor a perfect square on the left side:
(y + -3.833333334)(y + -3.833333334) = 11.361111117

Calculate the square root of the right side: 3.370624737

Break this problem into two subproblems by setting 
(y + -3.833333334) equal to 3.370624737 and -3.370624737.

Subproblem 1
y + -3.833333334 = 3.370624737

Simplifying
y + -3.833333334 = 3.370624737

Reorder the terms:
-3.833333334 + y = 3.370624737

Solving
-3.833333334 + y = 3.370624737

Solving for variable 'y'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + y = 3.370624737 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + y = 3.370624737 + 3.833333334
y = 3.370624737 + 3.833333334

Combine like terms: 3.370624737 + 3.833333334 = 7.203958071
y = 7.203958071

Simplifying
y = 7.203958071

Subproblem 2
y + -3.833333334 = -3.370624737

Simplifying
y + -3.833333334 = -3.370624737

Reorder the terms:
-3.833333334 + y = -3.370624737

Solving
-3.833333334 + y = -3.370624737

Solving for variable 'y'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + y = -3.370624737 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + y = -3.370624737 + 3.833333334
y = -3.370624737 + 3.833333334

Combine like terms: -3.370624737 + 3.833333334 = 0.462708597
y = 0.462708597

Simplifying
y = 0.462708597

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.203958071, 0.462708597}
Solution
y = {7.203958071, 0.462708597}