(3y-20)(y+10)70=180

Solution for (3y-20)(y+10)70=180 equation:

Simplifying
(3y + -20)(y + 10) * 70 = 180

Reorder the terms:
(-20 + 3y)(y + 10) * 70 = 180

Reorder the terms:
(-20 + 3y)(10 + y) * 70 = 180

Reorder the terms for easier multiplication:
70(-20 + 3y)(10 + y) = 180

Multiply (-20 + 3y) * (10 + y)
70(-20(10 + y) + 3y * (10 + y)) = 180
70((10 * -20 + y * -20) + 3y * (10 + y)) = 180
70((-200 + -20y) + 3y * (10 + y)) = 180
70(-200 + -20y + (10 * 3y + y * 3y)) = 180
70(-200 + -20y + (30y + 3y2)) = 180

Combine like terms: -20y + 30y = 10y
70(-200 + 10y + 3y2) = 180
(-200 * 70 + 10y * 70 + 3y2 * 70) = 180
(-14000 + 700y + 210y2) = 180

Solving
-14000 + 700y + 210y2 = 180

Solving for variable 'y'.

Reorder the terms:
-14000 + -180 + 700y + 210y2 = 180 + -180

Combine like terms: -14000 + -180 = -14180
-14180 + 700y + 210y2 = 180 + -180

Combine like terms: 180 + -180 = 0
-14180 + 700y + 210y2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-1418 + 70y + 21y2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-1418 + 70y + 21y2)' equal to zero and attempt to solve:

Simplifying
-1418 + 70y + 21y2 = 0

Solving
-1418 + 70y + 21y2 = 0

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

Divide each side by '21'.
-67.52380952 + 3.333333333y + y2 = 0

Move the constant term to the right:

Add '67.52380952' to each side of the equation.
-67.52380952 + 3.333333333y + 67.52380952 + y2 = 0 + 67.52380952

Reorder the terms:
-67.52380952 + 67.52380952 + 3.333333333y + y2 = 0 + 67.52380952

Combine like terms: -67.52380952 + 67.52380952 = 0.00000000
0.00000000 + 3.333333333y + y2 = 0 + 67.52380952
3.333333333y + y2 = 0 + 67.52380952

Combine like terms: 0 + 67.52380952 = 67.52380952
3.333333333y + y2 = 67.52380952

The y term is 3.333333333y.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333y + 2.777777779 + y2 = 67.52380952 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333y + y2 = 67.52380952 + 2.777777779

Combine like terms: 67.52380952 + 2.777777779 = 70.301587299
2.777777779 + 3.333333333y + y2 = 70.301587299

Factor a perfect square on the left side:
(y + 1.666666667)(y + 1.666666667) = 70.301587299

Calculate the square root of the right side: 8.384604183

Break this problem into two subproblems by setting 
(y + 1.666666667) equal to 8.384604183 and -8.384604183.

Subproblem 1
y + 1.666666667 = 8.384604183

Simplifying
y + 1.666666667 = 8.384604183

Reorder the terms:
1.666666667 + y = 8.384604183

Solving
1.666666667 + y = 8.384604183

Solving for variable 'y'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + y = 8.384604183 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + y = 8.384604183 + -1.666666667
y = 8.384604183 + -1.666666667

Combine like terms: 8.384604183 + -1.666666667 = 6.717937516
y = 6.717937516

Simplifying
y = 6.717937516

Subproblem 2
y + 1.666666667 = -8.384604183

Simplifying
y + 1.666666667 = -8.384604183

Reorder the terms:
1.666666667 + y = -8.384604183

Solving
1.666666667 + y = -8.384604183

Solving for variable 'y'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + y = -8.384604183 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + y = -8.384604183 + -1.666666667
y = -8.384604183 + -1.666666667

Combine like terms: -8.384604183 + -1.666666667 = -10.05127085
y = -10.05127085

Simplifying
y = -10.05127085

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.717937516, -10.05127085}
Solution
y = {6.717937516, -10.05127085}