4y(5y-2)=52

Simple and best practice solution for 4y(5y-2)=52 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 4y(5y-2)=52 equation: 


Simplifying
4y(5y + -2) = 52

Reorder the terms:
4y(-2 + 5y) = 52
(-2 * 4y + 5y * 4y) = 52
(-8y + 20y2) = 52

Solving
-8y + 20y2 = 52

Solving for variable 'y'.

Reorder the terms:
-52 + -8y + 20y2 = 52 + -52

Combine like terms: 52 + -52 = 0
-52 + -8y + 20y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-13 + -2y + 5y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-13 + -2y + 5y2)' equal to zero and attempt to solve:

Simplifying
-13 + -2y + 5y2 = 0

Solving
-13 + -2y + 5y2 = 0

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

Divide each side by '5'.
-2.6 + -0.4y + y2 = 0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + -0.4y + 2.6 + y2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + -0.4y + y2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + -0.4y + y2 = 0 + 2.6
-0.4y + y2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
-0.4y + y2 = 2.6

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 = 2.6 + 0.04

Reorder the terms:
0.04 + -0.4y + y2 = 2.6 + 0.04

Combine like terms: 2.6 + 0.04 = 2.64
0.04 + -0.4y + y2 = 2.64

Factor a perfect square on the left side:
(y + -0.2)(y + -0.2) = 2.64

Calculate the square root of the right side: 1.624807681

Break this problem into two subproblems by setting 
(y + -0.2) equal to 1.624807681 and -1.624807681.


Subproblem 1
y + -0.2 = 1.624807681

Simplifying
y + -0.2 = 1.624807681

Reorder the terms:
-0.2 + y = 1.624807681

Solving
-0.2 + y = 1.624807681

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 = 1.624807681 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + y = 1.624807681 + 0.2
y = 1.624807681 + 0.2

Combine like terms: 1.624807681 + 0.2 = 1.824807681
y = 1.824807681

Simplifying
y = 1.824807681


Subproblem 2
y + -0.2 = -1.624807681

Simplifying
y + -0.2 = -1.624807681

Reorder the terms:
-0.2 + y = -1.624807681

Solving
-0.2 + y = -1.624807681

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 = -1.624807681 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + y = -1.624807681 + 0.2
y = -1.624807681 + 0.2

Combine like terms: -1.624807681 + 0.2 = -1.424807681
y = -1.424807681

Simplifying
y = -1.424807681


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.824807681, -1.424807681}
Solution
y = {1.824807681, -1.424807681}

See similar equations:

| -57-2x=23-7x | | 78=2(m-3)+m | | 6x-10=4x-24 | | 80=-6x-5(-3x-7) | | 4+60/6 | | -4c-8=3c+8 | | 4+6z/6z=12 | | 4(3x-5)=6x+7-3x | | 5+2y=6y+25 | | -2(g+8)=6(3g-7) | | 106=4x+5x+7 | | -4x-4=x-34 | | 28-6m=3m-2m | | 5*6+2(6+9)= | | -4-4x=-34x | | 8y-5x=40 | | -2(g+8)=6(3g-1) | | -7(2r+6)+9(4r+4)= | | 1/3(6*6+9) | | 192/5.3 | | 5.3/192 | | 2(24x)=10.5x | | 3.16/192 | | (2a+1)*(2a-1)= | | r-11=4+4r | | r-11=4+4 | | -2-m/2+n | | 6K(K+2)=K-3 | | 4x+7-5x=-1 | | 16/3/192 | | 45=-5(2-x)-5 | | 4(x+2)+3(4+x)-4=7x |

Equations solver categories