10y+18=-3(5y-7)5y

Solution for 10y+18=-3(5y-7)5y equation:

Simplifying
10y + 18 = -3(5y + -7) * 5y

Reorder the terms:
18 + 10y = -3(5y + -7) * 5y

Reorder the terms:
18 + 10y = -3(-7 + 5y) * 5y

Reorder the terms for easier multiplication:
18 + 10y = -3 * 5y(-7 + 5y)

Multiply -3 * 5
18 + 10y = -15y(-7 + 5y)
18 + 10y = (-7 * -15y + 5y * -15y)
18 + 10y = (105y + -75y2)

Solving
18 + 10y = 105y + -75y2

Solving for variable 'y'.

Combine like terms: 10y + -105y = -95y
18 + -95y + 75y2 = 105y + -75y2 + -105y + 75y2

Reorder the terms:
18 + -95y + 75y2 = 105y + -105y + -75y2 + 75y2

Combine like terms: 105y + -105y = 0
18 + -95y + 75y2 = 0 + -75y2 + 75y2
18 + -95y + 75y2 = -75y2 + 75y2

Combine like terms: -75y2 + 75y2 = 0
18 + -95y + 75y2 = 0

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

Divide each side by '75'.
0.24 + -1.266666667y + y2 = 0

Move the constant term to the right:

Add '-0.24' to each side of the equation.
0.24 + -1.266666667y + -0.24 + y2 = 0 + -0.24

Reorder the terms:
0.24 + -0.24 + -1.266666667y + y2 = 0 + -0.24

Combine like terms: 0.24 + -0.24 = 0.00
0.00 + -1.266666667y + y2 = 0 + -0.24
-1.266666667y + y2 = 0 + -0.24

Combine like terms: 0 + -0.24 = -0.24
-1.266666667y + y2 = -0.24

The y term is -1.266666667y.  Take half its coefficient (-0.6333333335).
Square it (0.4011111113) and add it to both sides.

Add '0.4011111113' to each side of the equation.
-1.266666667y + 0.4011111113 + y2 = -0.24 + 0.4011111113

Reorder the terms:
0.4011111113 + -1.266666667y + y2 = -0.24 + 0.4011111113

Combine like terms: -0.24 + 0.4011111113 = 0.1611111113
0.4011111113 + -1.266666667y + y2 = 0.1611111113

Factor a perfect square on the left side:
(y + -0.6333333335)(y + -0.6333333335) = 0.1611111113

Calculate the square root of the right side: 0.401386486

Break this problem into two subproblems by setting 
(y + -0.6333333335) equal to 0.401386486 and -0.401386486.

Subproblem 1
y + -0.6333333335 = 0.401386486

Simplifying
y + -0.6333333335 = 0.401386486

Reorder the terms:
-0.6333333335 + y = 0.401386486

Solving
-0.6333333335 + y = 0.401386486

Solving for variable 'y'.

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

Add '0.6333333335' to each side of the equation.
-0.6333333335 + 0.6333333335 + y = 0.401386486 + 0.6333333335

Combine like terms: -0.6333333335 + 0.6333333335 = 0.0000000000
0.0000000000 + y = 0.401386486 + 0.6333333335
y = 0.401386486 + 0.6333333335

Combine like terms: 0.401386486 + 0.6333333335 = 1.0347198195
y = 1.0347198195

Simplifying
y = 1.0347198195

Subproblem 2
y + -0.6333333335 = -0.401386486

Simplifying
y + -0.6333333335 = -0.401386486

Reorder the terms:
-0.6333333335 + y = -0.401386486

Solving
-0.6333333335 + y = -0.401386486

Solving for variable 'y'.

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

Add '0.6333333335' to each side of the equation.
-0.6333333335 + 0.6333333335 + y = -0.401386486 + 0.6333333335

Combine like terms: -0.6333333335 + 0.6333333335 = 0.0000000000
0.0000000000 + y = -0.401386486 + 0.6333333335
y = -0.401386486 + 0.6333333335

Combine like terms: -0.401386486 + 0.6333333335 = 0.2319468475
y = 0.2319468475

Simplifying
y = 0.2319468475

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.0347198195, 0.2319468475}