10y(5y+8)=42

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Solution for 10y(5y+8)=42 equation: 


Simplifying
10y(5y + 8) = 42

Reorder the terms:
10y(8 + 5y) = 42
(8 * 10y + 5y * 10y) = 42
(80y + 50y2) = 42

Solving
80y + 50y2 = 42

Solving for variable 'y'.

Reorder the terms:
-42 + 80y + 50y2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 80y + 50y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 40y + 25y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-21 + 40y + 25y2)' equal to zero and attempt to solve:

Simplifying
-21 + 40y + 25y2 = 0

Solving
-21 + 40y + 25y2 = 0

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

Divide each side by '25'.
-0.84 + 1.6y + y2 = 0

Move the constant term to the right:

Add '0.84' to each side of the equation.
-0.84 + 1.6y + 0.84 + y2 = 0 + 0.84

Reorder the terms:
-0.84 + 0.84 + 1.6y + y2 = 0 + 0.84

Combine like terms: -0.84 + 0.84 = 0.00
0.00 + 1.6y + y2 = 0 + 0.84
1.6y + y2 = 0 + 0.84

Combine like terms: 0 + 0.84 = 0.84
1.6y + y2 = 0.84

The y term is 1.6y.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6y + 0.64 + y2 = 0.84 + 0.64

Reorder the terms:
0.64 + 1.6y + y2 = 0.84 + 0.64

Combine like terms: 0.84 + 0.64 = 1.48
0.64 + 1.6y + y2 = 1.48

Factor a perfect square on the left side:
(y + 0.8)(y + 0.8) = 1.48

Calculate the square root of the right side: 1.216552506

Break this problem into two subproblems by setting 
(y + 0.8) equal to 1.216552506 and -1.216552506.


Subproblem 1
y + 0.8 = 1.216552506

Simplifying
y + 0.8 = 1.216552506

Reorder the terms:
0.8 + y = 1.216552506

Solving
0.8 + y = 1.216552506

Solving for variable 'y'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + y = 1.216552506 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + y = 1.216552506 + -0.8
y = 1.216552506 + -0.8

Combine like terms: 1.216552506 + -0.8 = 0.416552506
y = 0.416552506

Simplifying
y = 0.416552506


Subproblem 2
y + 0.8 = -1.216552506

Simplifying
y + 0.8 = -1.216552506

Reorder the terms:
0.8 + y = -1.216552506

Solving
0.8 + y = -1.216552506

Solving for variable 'y'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + y = -1.216552506 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + y = -1.216552506 + -0.8
y = -1.216552506 + -0.8

Combine like terms: -1.216552506 + -0.8 = -2.016552506
y = -2.016552506

Simplifying
y = -2.016552506


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.416552506, -2.016552506}
Solution
y = {0.416552506, -2.016552506}

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