(y+2)(y+3)-1=0

Simple and best practice solution for (y+2)(y+3)-1=0 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 (y+2)(y+3)-1=0 equation:


Simplifying
(y + 2)(y + 3) + -1 = 0

Reorder the terms:
(2 + y)(y + 3) + -1 = 0

Reorder the terms:
(2 + y)(3 + y) + -1 = 0

Multiply (2 + y) * (3 + y)
(2(3 + y) + y(3 + y)) + -1 = 0
((3 * 2 + y * 2) + y(3 + y)) + -1 = 0
((6 + 2y) + y(3 + y)) + -1 = 0
(6 + 2y + (3 * y + y * y)) + -1 = 0
(6 + 2y + (3y + y2)) + -1 = 0

Combine like terms: 2y + 3y = 5y
(6 + 5y + y2) + -1 = 0

Reorder the terms:
6 + -1 + 5y + y2 = 0

Combine like terms: 6 + -1 = 5
5 + 5y + y2 = 0

Solving
5 + 5y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 5y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + 5y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 5y + y2 = 0 + -5
5y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
5y + y2 = -5

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = -5 + 6.25

Reorder the terms:
6.25 + 5y + y2 = -5 + 6.25

Combine like terms: -5 + 6.25 = 1.25
6.25 + 5y + y2 = 1.25

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(y + 2.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

y + 2.5 = 1.118033989 Simplifying y + 2.5 = 1.118033989 Reorder the terms: 2.5 + y = 1.118033989 Solving 2.5 + y = 1.118033989 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = 1.118033989 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 1.118033989 + -2.5 y = 1.118033989 + -2.5 Combine like terms: 1.118033989 + -2.5 = -1.381966011 y = -1.381966011 Simplifying y = -1.381966011

Subproblem 2

y + 2.5 = -1.118033989 Simplifying y + 2.5 = -1.118033989 Reorder the terms: 2.5 + y = -1.118033989 Solving 2.5 + y = -1.118033989 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = -1.118033989 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -1.118033989 + -2.5 y = -1.118033989 + -2.5 Combine like terms: -1.118033989 + -2.5 = -3.618033989 y = -3.618033989 Simplifying y = -3.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-1.381966011, -3.618033989}

See similar equations:

| X(x-8)=5x | | 91-4x=2x+7 | | xy+y+1=y | | xy+y+1=1 | | 9(x-7)=7x-67 | | 5x+3-5=70-27 | | (n+2)*3=18 | | (x-5)(x-1)(x-2)=0 | | (n-6)*2=6 | | 3(a+4)-2a=7(a+6) | | (n+1)*10=20 | | 32-3x=41 | | 6x=2y-18 | | .333x-.25x+.083x=3 | | abs(2x-3)=14 | | abs(x^2-9)=x-1 | | 15b+12b^2= | | -6x+9x-8x=0 | | 6(4x+3)+6(4x+4)+6=48x+48 | | 6x+9x-8x=0 | | 10p+2+3p= | | 10x-6y=-2 | | 7(n+5)=84 | | 3-2x=4x+8 | | 15x+12x^2= | | 20-x=14 | | 3y^2-7-6=0 | | 2y=10x+8 | | v^2+3v-12=0 | | 61/6=61/4 | | 22-2x=16 | | 20-x=4 |

Equations solver categories