(3x+1)(x+5)=2

Simple and best practice solution for (3x+1)(x+5)=2 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 (3x+1)(x+5)=2 equation: 


Simplifying
(3x + 1)(x + 5) = 2

Reorder the terms:
(1 + 3x)(x + 5) = 2

Reorder the terms:
(1 + 3x)(5 + x) = 2

Multiply (1 + 3x) * (5 + x)
(1(5 + x) + 3x * (5 + x)) = 2
((5 * 1 + x * 1) + 3x * (5 + x)) = 2
((5 + 1x) + 3x * (5 + x)) = 2
(5 + 1x + (5 * 3x + x * 3x)) = 2
(5 + 1x + (15x + 3x2)) = 2

Combine like terms: 1x + 15x = 16x
(5 + 16x + 3x2) = 2

Solving
5 + 16x + 3x2 = 2

Solving for variable 'x'.

Reorder the terms:
5 + -2 + 16x + 3x2 = 2 + -2

Combine like terms: 5 + -2 = 3
3 + 16x + 3x2 = 2 + -2

Combine like terms: 2 + -2 = 0
3 + 16x + 3x2 = 0

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

Divide each side by '3'.
1 + 5.333333333x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 5.333333333x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 5.333333333x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5.333333333x + x2 = 0 + -1
5.333333333x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
5.333333333x + x2 = -1

The x term is 5.333333333x.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333x + 7.111111113 + x2 = -1 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333x + x2 = -1 + 7.111111113

Combine like terms: -1 + 7.111111113 = 6.111111113
7.111111113 + 5.333333333x + x2 = 6.111111113

Factor a perfect square on the left side:
(x + 2.666666667)(x + 2.666666667) = 6.111111113

Calculate the square root of the right side: 2.472066163

Break this problem into two subproblems by setting 
(x + 2.666666667) equal to 2.472066163 and -2.472066163.


Subproblem 1
x + 2.666666667 = 2.472066163

Simplifying
x + 2.666666667 = 2.472066163

Reorder the terms:
2.666666667 + x = 2.472066163

Solving
2.666666667 + x = 2.472066163

Solving for variable 'x'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = 2.472066163 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = 2.472066163 + -2.666666667
x = 2.472066163 + -2.666666667

Combine like terms: 2.472066163 + -2.666666667 = -0.194600504
x = -0.194600504

Simplifying
x = -0.194600504


Subproblem 2
x + 2.666666667 = -2.472066163

Simplifying
x + 2.666666667 = -2.472066163

Reorder the terms:
2.666666667 + x = -2.472066163

Solving
2.666666667 + x = -2.472066163

Solving for variable 'x'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = -2.472066163 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = -2.472066163 + -2.666666667
x = -2.472066163 + -2.666666667

Combine like terms: -2.472066163 + -2.666666667 = -5.13873283
x = -5.13873283

Simplifying
x = -5.13873283


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.194600504, -5.13873283}

See similar equations:

| (3x/4)-2=12 | | 13x+50=11 | | -b-3=-5b+b | | 3y-2y-1/6=-1 | | 3(3n+4)=9(3n+2)+6 | | 6(x-3)=4times-7 | | X=-8+-2y | | 7(t-2)-8(2t+9)=-10(t+8)-9 | | 2.5=4.1-0.8x | | 1-4r=-4r | | 3x-4(7x+10)=92 | | 2x+200=0 | | -1/4=y-1/8 | | -4(5x-2)=-5 | | 2n+2=4+n | | 5r+29=4(3r+2) | | f(z)=z^2+1+i | | 5/6c=15 | | 5+6x=-4+9x | | (X+6)+(x-2)=62 | | 0=1-3cos(2x) | | 2x+6x-9=7 | | -6y+7y=22 | | -12=y+8 | | 4(4x+1)=5(6x-1) | | 4/3x3.14x8 | | 16x-8=15x-11 | | .5x+.25(x+16)=4+.75x | | 13+6x=8x+1 | | x-15=2/3x | | 6-r=6(1-3r) | | 5x+3a=4b |

Equations solver categories