5y(4y+2)=148

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Solution for 5y(4y+2)=148 equation: 


Simplifying
5y(4y + 2) = 148

Reorder the terms:
5y(2 + 4y) = 148
(2 * 5y + 4y * 5y) = 148
(10y + 20y2) = 148

Solving
10y + 20y2 = 148

Solving for variable 'y'.

Reorder the terms:
-148 + 10y + 20y2 = 148 + -148

Combine like terms: 148 + -148 = 0
-148 + 10y + 20y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-74 + 5y + 10y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-74 + 5y + 10y2)' equal to zero and attempt to solve:

Simplifying
-74 + 5y + 10y2 = 0

Solving
-74 + 5y + 10y2 = 0

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

Divide each side by '10'.
-7.4 + 0.5y + y2 = 0.0

Move the constant term to the right:

Add '7.4' to each side of the equation.
-7.4 + 0.5y + 7.4 + y2 = 0.0 + 7.4

Reorder the terms:
-7.4 + 7.4 + 0.5y + y2 = 0.0 + 7.4

Combine like terms: -7.4 + 7.4 = 0.0
0.0 + 0.5y + y2 = 0.0 + 7.4
0.5y + y2 = 0.0 + 7.4

Combine like terms: 0.0 + 7.4 = 7.4
0.5y + y2 = 7.4

The y term is 0.5y.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5y + 0.0625 + y2 = 7.4 + 0.0625

Reorder the terms:
0.0625 + 0.5y + y2 = 7.4 + 0.0625

Combine like terms: 7.4 + 0.0625 = 7.4625
0.0625 + 0.5y + y2 = 7.4625

Factor a perfect square on the left side:
(y + 0.25)(y + 0.25) = 7.4625

Calculate the square root of the right side: 2.731757676

Break this problem into two subproblems by setting 
(y + 0.25) equal to 2.731757676 and -2.731757676.


Subproblem 1
y + 0.25 = 2.731757676

Simplifying
y + 0.25 = 2.731757676

Reorder the terms:
0.25 + y = 2.731757676

Solving
0.25 + y = 2.731757676

Solving for variable 'y'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = 2.731757676 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = 2.731757676 + -0.25
y = 2.731757676 + -0.25

Combine like terms: 2.731757676 + -0.25 = 2.481757676
y = 2.481757676

Simplifying
y = 2.481757676


Subproblem 2
y + 0.25 = -2.731757676

Simplifying
y + 0.25 = -2.731757676

Reorder the terms:
0.25 + y = -2.731757676

Solving
0.25 + y = -2.731757676

Solving for variable 'y'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = -2.731757676 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = -2.731757676 + -0.25
y = -2.731757676 + -0.25

Combine like terms: -2.731757676 + -0.25 = -2.981757676
y = -2.981757676

Simplifying
y = -2.981757676


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.481757676, -2.981757676}
Solution
y = {2.481757676, -2.981757676}

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