5y^2-10y-23=-7

Solution for 5y^2-10y-23=-7 equation:

Simplifying
5y2 + -10y + -23 = -7

Reorder the terms:
-23 + -10y + 5y2 = -7

Solving
-23 + -10y + 5y2 = -7

Solving for variable 'y'.

Reorder the terms:
-23 + 7 + -10y + 5y2 = -7 + 7

Combine like terms: -23 + 7 = -16
-16 + -10y + 5y2 = -7 + 7

Combine like terms: -7 + 7 = 0
-16 + -10y + 5y2 = 0

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

Divide each side by '5'.
-3.2 + -2y + y2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + -2y + 3.2 + y2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + -2y + y2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + -2y + y2 = 0 + 3.2
-2y + y2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
-2y + y2 = 3.2

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 3.2 + 1

Reorder the terms:
1 + -2y + y2 = 3.2 + 1

Combine like terms: 3.2 + 1 = 4.2
1 + -2y + y2 = 4.2

Factor a perfect square on the left side:
(y + -1)(y + -1) = 4.2

Calculate the square root of the right side: 2.049390153

Break this problem into two subproblems by setting 
(y + -1) equal to 2.049390153 and -2.049390153.

Subproblem 1
y + -1 = 2.049390153

Simplifying
y + -1 = 2.049390153

Reorder the terms:
-1 + y = 2.049390153

Solving
-1 + y = 2.049390153

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 2.049390153 + 1

Combine like terms: -1 + 1 = 0
0 + y = 2.049390153 + 1
y = 2.049390153 + 1

Combine like terms: 2.049390153 + 1 = 3.049390153
y = 3.049390153

Simplifying
y = 3.049390153

Subproblem 2
y + -1 = -2.049390153

Simplifying
y + -1 = -2.049390153

Reorder the terms:
-1 + y = -2.049390153

Solving
-1 + y = -2.049390153

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -2.049390153 + 1

Combine like terms: -1 + 1 = 0
0 + y = -2.049390153 + 1
y = -2.049390153 + 1

Combine like terms: -2.049390153 + 1 = -1.049390153
y = -1.049390153

Simplifying
y = -1.049390153

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.049390153, -1.049390153}