4y(5y-2)=48

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Solution for 4y(5y-2)=48 equation: 


Simplifying
4y(5y + -2) = 48

Reorder the terms:
4y(-2 + 5y) = 48
(-2 * 4y + 5y * 4y) = 48
(-8y + 20y2) = 48

Solving
-8y + 20y2 = 48

Solving for variable 'y'.

Reorder the terms:
-48 + -8y + 20y2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + -8y + 20y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + -2y + 5y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-12 + -2y + 5y2)' equal to zero and attempt to solve:

Simplifying
-12 + -2y + 5y2 = 0

Solving
-12 + -2y + 5y2 = 0

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

Divide each side by '5'.
-2.4 + -0.4y + y2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + -0.4y + 2.4 + y2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + -0.4y + y2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + -0.4y + y2 = 0 + 2.4
-0.4y + y2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
-0.4y + y2 = 2.4

The y term is -0.4y.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4y + 0.04 + y2 = 2.4 + 0.04

Reorder the terms:
0.04 + -0.4y + y2 = 2.4 + 0.04

Combine like terms: 2.4 + 0.04 = 2.44
0.04 + -0.4y + y2 = 2.44

Factor a perfect square on the left side:
(y + -0.2)(y + -0.2) = 2.44

Calculate the square root of the right side: 1.562049935

Break this problem into two subproblems by setting 
(y + -0.2) equal to 1.562049935 and -1.562049935.


Subproblem 1
y + -0.2 = 1.562049935

Simplifying
y + -0.2 = 1.562049935

Reorder the terms:
-0.2 + y = 1.562049935

Solving
-0.2 + y = 1.562049935

Solving for variable 'y'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + y = 1.562049935 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + y = 1.562049935 + 0.2
y = 1.562049935 + 0.2

Combine like terms: 1.562049935 + 0.2 = 1.762049935
y = 1.762049935

Simplifying
y = 1.762049935


Subproblem 2
y + -0.2 = -1.562049935

Simplifying
y + -0.2 = -1.562049935

Reorder the terms:
-0.2 + y = -1.562049935

Solving
-0.2 + y = -1.562049935

Solving for variable 'y'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + y = -1.562049935 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + y = -1.562049935 + 0.2
y = -1.562049935 + 0.2

Combine like terms: -1.562049935 + 0.2 = -1.362049935
y = -1.362049935

Simplifying
y = -1.362049935


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.762049935, -1.362049935}
Solution
y = {1.762049935, -1.362049935}

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