4y(2y+3)=16

Simple and best practice solution for 4y(2y+3)=16 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(2y+3)=16 equation: 


Simplifying
4y(2y + 3) = 16

Reorder the terms:
4y(3 + 2y) = 16
(3 * 4y + 2y * 4y) = 16
(12y + 8y2) = 16

Solving
12y + 8y2 = 16

Solving for variable 'y'.

Reorder the terms:
-16 + 12y + 8y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 12y + 8y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 3y + 2y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-4 + 3y + 2y2)' equal to zero and attempt to solve:

Simplifying
-4 + 3y + 2y2 = 0

Solving
-4 + 3y + 2y2 = 0

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

Divide each side by '2'.
-2 + 1.5y + y2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 1.5y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + 1.5y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 1.5y + y2 = 0 + 2
1.5y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
1.5y + y2 = 2

The y term is 1.5y.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5y + 0.5625 + y2 = 2 + 0.5625

Reorder the terms:
0.5625 + 1.5y + y2 = 2 + 0.5625

Combine like terms: 2 + 0.5625 = 2.5625
0.5625 + 1.5y + y2 = 2.5625

Factor a perfect square on the left side:
(y + 0.75)(y + 0.75) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(y + 0.75) equal to 1.600781059 and -1.600781059.


Subproblem 1
y + 0.75 = 1.600781059

Simplifying
y + 0.75 = 1.600781059

Reorder the terms:
0.75 + y = 1.600781059

Solving
0.75 + y = 1.600781059

Solving for variable 'y'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + y = 1.600781059 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + y = 1.600781059 + -0.75
y = 1.600781059 + -0.75

Combine like terms: 1.600781059 + -0.75 = 0.850781059
y = 0.850781059

Simplifying
y = 0.850781059


Subproblem 2
y + 0.75 = -1.600781059

Simplifying
y + 0.75 = -1.600781059

Reorder the terms:
0.75 + y = -1.600781059

Solving
0.75 + y = -1.600781059

Solving for variable 'y'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + y = -1.600781059 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + y = -1.600781059 + -0.75
y = -1.600781059 + -0.75

Combine like terms: -1.600781059 + -0.75 = -2.350781059
y = -2.350781059

Simplifying
y = -2.350781059


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.850781059, -2.350781059}
Solution
y = {0.850781059, -2.350781059}

See similar equations:

| 2.2s-6.2=0.8s+13.12 | | 2/3x-18=8 | | 6x-3+12=24 | | 2a(b+3+6bc)= | | 16-5=n | | s+s=8 | | 2b+6a+12abc= | | 90-x=.25(x) | | 4m-(-6)= | | -4v+11= | | X-6=-4+8 | | 5l-15=24+3l-1 | | 6(2l+7)=66 | | 4c+5d-2c+3c= | | 0=16t^2+0t+16 | | 5.1(x+2)= | | x^2+307=0 | | 0.12p+20=80 | | (x-3)(5-2x)=0 | | 3/4n=15 | | K/3.14=7.1 | | 0.5x=3.15 | | -10(s+2)=-48 | | x+2x=0.23 | | x=(4x+8y) | | -7-x=-2x | | 9w-14w=35 | | 25/16z=4 | | x^2+4x^2+4x-15=0 | | 4c=7.2 | | 2(2l+9)=46 | | 3d+6=12ford |

Equations solver categories