5y+7=2y(2y+3)(3*13)

Solution for 5y+7=2y(2y+3)(3*13) equation:

Simplifying
5y + 7 = 2y(2y + 3)(3 * 13)

Reorder the terms:
7 + 5y = 2y(2y + 3)(3 * 13)

Reorder the terms:
7 + 5y = 2y(3 + 2y)(3 * 13)

Multiply 3 * 13
7 + 5y = 2y(3 + 2y)(39)

Reorder the terms for easier multiplication:
7 + 5y = 2 * 39y(3 + 2y)

Multiply 2 * 39
7 + 5y = 78y(3 + 2y)
7 + 5y = (3 * 78y + 2y * 78y)
7 + 5y = (234y + 156y2)

Solving
7 + 5y = 234y + 156y2

Solving for variable 'y'.

Combine like terms: 5y + -234y = -229y
7 + -229y + -156y2 = 234y + 156y2 + -234y + -156y2

Reorder the terms:
7 + -229y + -156y2 = 234y + -234y + 156y2 + -156y2

Combine like terms: 234y + -234y = 0
7 + -229y + -156y2 = 0 + 156y2 + -156y2
7 + -229y + -156y2 = 156y2 + -156y2

Combine like terms: 156y2 + -156y2 = 0
7 + -229y + -156y2 = 0

Begin completing the square.  Divide all terms by
-156 the coefficient of the squared term: 

Divide each side by '-156'.
-0.04487179487 + 1.467948718y + y2 = 0

Move the constant term to the right:

Add '0.04487179487' to each side of the equation.
-0.04487179487 + 1.467948718y + 0.04487179487 + y2 = 0 + 0.04487179487

Reorder the terms:
-0.04487179487 + 0.04487179487 + 1.467948718y + y2 = 0 + 0.04487179487

Combine like terms: -0.04487179487 + 0.04487179487 = 0.00000000000
0.00000000000 + 1.467948718y + y2 = 0 + 0.04487179487
1.467948718y + y2 = 0 + 0.04487179487

Combine like terms: 0 + 0.04487179487 = 0.04487179487
1.467948718y + y2 = 0.04487179487

The y term is 1.467948718y.  Take half its coefficient (0.733974359).
Square it (0.5387183597) and add it to both sides.

Add '0.5387183597' to each side of the equation.
1.467948718y + 0.5387183597 + y2 = 0.04487179487 + 0.5387183597

Reorder the terms:
0.5387183597 + 1.467948718y + y2 = 0.04487179487 + 0.5387183597

Combine like terms: 0.04487179487 + 0.5387183597 = 0.58359015457
0.5387183597 + 1.467948718y + y2 = 0.58359015457

Factor a perfect square on the left side:
(y + 0.733974359)(y + 0.733974359) = 0.58359015457

Calculate the square root of the right side: 0.763930726

Break this problem into two subproblems by setting 
(y + 0.733974359) equal to 0.763930726 and -0.763930726.

Subproblem 1
y + 0.733974359 = 0.763930726

Simplifying
y + 0.733974359 = 0.763930726

Reorder the terms:
0.733974359 + y = 0.763930726

Solving
0.733974359 + y = 0.763930726

Solving for variable 'y'.

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

Add '-0.733974359' to each side of the equation.
0.733974359 + -0.733974359 + y = 0.763930726 + -0.733974359

Combine like terms: 0.733974359 + -0.733974359 = 0.000000000
0.000000000 + y = 0.763930726 + -0.733974359
y = 0.763930726 + -0.733974359

Combine like terms: 0.763930726 + -0.733974359 = 0.029956367
y = 0.029956367

Simplifying
y = 0.029956367

Subproblem 2
y + 0.733974359 = -0.763930726

Simplifying
y + 0.733974359 = -0.763930726

Reorder the terms:
0.733974359 + y = -0.763930726

Solving
0.733974359 + y = -0.763930726

Solving for variable 'y'.

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

Add '-0.733974359' to each side of the equation.
0.733974359 + -0.733974359 + y = -0.763930726 + -0.733974359

Combine like terms: 0.733974359 + -0.733974359 = 0.000000000
0.000000000 + y = -0.763930726 + -0.733974359
y = -0.763930726 + -0.733974359

Combine like terms: -0.763930726 + -0.733974359 = -1.497905085
y = -1.497905085

Simplifying
y = -1.497905085

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.029956367, -1.497905085}