5y(y+1)=4(y+2)-6

Simple and best practice solution for 5y(y+1)=4(y+2)-6 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 5y(y+1)=4(y+2)-6 equation: 


Simplifying
5y(y + 1) = 4(y + 2) + -6

Reorder the terms:
5y(1 + y) = 4(y + 2) + -6
(1 * 5y + y * 5y) = 4(y + 2) + -6
(5y + 5y2) = 4(y + 2) + -6

Reorder the terms:
5y + 5y2 = 4(2 + y) + -6
5y + 5y2 = (2 * 4 + y * 4) + -6
5y + 5y2 = (8 + 4y) + -6

Reorder the terms:
5y + 5y2 = 8 + -6 + 4y

Combine like terms: 8 + -6 = 2
5y + 5y2 = 2 + 4y

Solving
5y + 5y2 = 2 + 4y

Solving for variable 'y'.

Reorder the terms:
-2 + 5y + -4y + 5y2 = 2 + 4y + -2 + -4y

Combine like terms: 5y + -4y = 1y
-2 + 1y + 5y2 = 2 + 4y + -2 + -4y

Reorder the terms:
-2 + 1y + 5y2 = 2 + -2 + 4y + -4y

Combine like terms: 2 + -2 = 0
-2 + 1y + 5y2 = 0 + 4y + -4y
-2 + 1y + 5y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-2 + 1y + 5y2 = 0

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

Divide each side by '5'.
-0.4 + 0.2y + y2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.2y + 0.4 + y2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.2y + y2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.2y + y2 = 0 + 0.4
0.2y + y2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.2y + y2 = 0.4

The y term is 0.2y.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2y + 0.01 + y2 = 0.4 + 0.01

Reorder the terms:
0.01 + 0.2y + y2 = 0.4 + 0.01

Combine like terms: 0.4 + 0.01 = 0.41
0.01 + 0.2y + y2 = 0.41

Factor a perfect square on the left side:
(y + 0.1)(y + 0.1) = 0.41

Calculate the square root of the right side: 0.640312424

Break this problem into two subproblems by setting 
(y + 0.1) equal to 0.640312424 and -0.640312424.


Subproblem 1
y + 0.1 = 0.640312424

Simplifying
y + 0.1 = 0.640312424

Reorder the terms:
0.1 + y = 0.640312424

Solving
0.1 + y = 0.640312424

Solving for variable 'y'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + y = 0.640312424 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + y = 0.640312424 + -0.1
y = 0.640312424 + -0.1

Combine like terms: 0.640312424 + -0.1 = 0.540312424
y = 0.540312424

Simplifying
y = 0.540312424


Subproblem 2
y + 0.1 = -0.640312424

Simplifying
y + 0.1 = -0.640312424

Reorder the terms:
0.1 + y = -0.640312424

Solving
0.1 + y = -0.640312424

Solving for variable 'y'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + y = -0.640312424 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + y = -0.640312424 + -0.1
y = -0.640312424 + -0.1

Combine like terms: -0.640312424 + -0.1 = -0.740312424
y = -0.740312424

Simplifying
y = -0.740312424


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.540312424, -0.740312424}

See similar equations:

| -3x-7.1-4.2x-4.6x+2= | | 8p+1=17 | | A=3+25-7(5) | | 16x-108=180 | | 1/2x+x=18 | | b^3+6b^2=0 | | 4x^4-20x=0 | | 5x^2-55x=140 | | 8x-39=8x-69 | | 20x^2-125=0 | | 6(a-6)=5(a+4) | | 2w+5x-y+8w-19x-7x= | | (x^2-74)/(x-8) | | 5/10*10/3 | | (9/(x-3))=(3x/(x-3)) | | -120+x^2-2x=0 | | 5/10/10/3 | | y-26=18 | | (5X-4)+3(X+2)=90 | | 6w+7y+11x+3x-15y+4w= | | -2000000+(-800000x)=-4200000 | | 27+x=x*4 | | 3w+6x-11y+7w+8x+3y= | | -2000000+(-800000x)=-3600000 | | X^2=2x+120 | | -26=c/13 | | 5/10x10/3 | | 11x-2y+12w-6y-2w+3x= | | 7w-12+6w-14=39 | | 4x^2+31x-8=0 | | 4+2x=3x-1 | | 5a+b/a+3a |

Equations solver categories