(6+2x)(12+2x)=180

Simple and best practice solution for (6+2x)(12+2x)=180 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 (6+2x)(12+2x)=180 equation: 


Simplifying
(6 + 2x)(12 + 2x) = 180

Multiply (6 + 2x) * (12 + 2x)
(6(12 + 2x) + 2x * (12 + 2x)) = 180
((12 * 6 + 2x * 6) + 2x * (12 + 2x)) = 180
((72 + 12x) + 2x * (12 + 2x)) = 180
(72 + 12x + (12 * 2x + 2x * 2x)) = 180
(72 + 12x + (24x + 4x2)) = 180

Combine like terms: 12x + 24x = 36x
(72 + 36x + 4x2) = 180

Solving
72 + 36x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
72 + -180 + 36x + 4x2 = 180 + -180

Combine like terms: 72 + -180 = -108
-108 + 36x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-108 + 36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-27 + 9x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-27 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
-27 + 9x + x2 = 0

Solving
-27 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 9x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + 9x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 9x + x2 = 0 + 27
9x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
9x + x2 = 27

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 27 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 27 + 20.25

Combine like terms: 27 + 20.25 = 47.25
20.25 + 9x + x2 = 47.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(x + 4.5) equal to 6.873863542 and -6.873863542.


Subproblem 1
x + 4.5 = 6.873863542

Simplifying
x + 4.5 = 6.873863542

Reorder the terms:
4.5 + x = 6.873863542

Solving
4.5 + x = 6.873863542

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 6.873863542 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 6.873863542 + -4.5
x = 6.873863542 + -4.5

Combine like terms: 6.873863542 + -4.5 = 2.373863542
x = 2.373863542

Simplifying
x = 2.373863542


Subproblem 2
x + 4.5 = -6.873863542

Simplifying
x + 4.5 = -6.873863542

Reorder the terms:
4.5 + x = -6.873863542

Solving
4.5 + x = -6.873863542

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -6.873863542 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -6.873863542 + -4.5
x = -6.873863542 + -4.5

Combine like terms: -6.873863542 + -4.5 = -11.373863542
x = -11.373863542

Simplifying
x = -11.373863542


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.373863542, -11.373863542}
Solution
x = {2.373863542, -11.373863542}

See similar equations:

| 5+3(2x+1)=-166 | | .5x^2-3x= | | 5(-8x+3)=-18-7x | | 84=2(5x+2) | | 8x^2-24x-4=0 | | 3x^2-12x+38=-3x^2-10x | | 4x(-x-3)=2(-2x-2)-2 | | 5xy(-2x)(-3y)= | | -34+(-36)= | | 5(1-4k)=-115 | | -(15m^2+6m^3)-(-5m)= | | -(13m^2+6m^3)-(-5m)= | | 19-(-5)= | | 3x+(2x-y)=31 | | 18+(-25)= | | 9x^2-16x+8=0 | | -8a-6(2a-1)=86 | | 17x+4=33.1+22.3x | | 8p-16=0 | | 6Ln(4x)=24 | | 13n^2-17=0 | | h^2-8+3h+10=0 | | -4k-5(5k+2)=-155 | | (-7b+6)-(2b-2)= | | 1x=0.625 | | 13=2(2x-7) | | 4b+-3d=n | | (5t-6)=(t+1)+2 | | 2(3x-2x)=x-4 | | 1x=-0.625 | | z+19=149z | | xy+4y-396=0 |

Equations solver categories