(3k-6)(3k+12)=4k-8k+12

Simple and best practice solution for (3k-6)(3k+12)=4k-8k+12 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 (3k-6)(3k+12)=4k-8k+12 equation: 


Simplifying
(3k + -6)(3k + 12) = 4k + -8k + 12

Reorder the terms:
(-6 + 3k)(3k + 12) = 4k + -8k + 12

Reorder the terms:
(-6 + 3k)(12 + 3k) = 4k + -8k + 12

Multiply (-6 + 3k) * (12 + 3k)
(-6(12 + 3k) + 3k * (12 + 3k)) = 4k + -8k + 12
((12 * -6 + 3k * -6) + 3k * (12 + 3k)) = 4k + -8k + 12
((-72 + -18k) + 3k * (12 + 3k)) = 4k + -8k + 12
(-72 + -18k + (12 * 3k + 3k * 3k)) = 4k + -8k + 12
(-72 + -18k + (36k + 9k2)) = 4k + -8k + 12

Combine like terms: -18k + 36k = 18k
(-72 + 18k + 9k2) = 4k + -8k + 12

Reorder the terms:
-72 + 18k + 9k2 = 12 + 4k + -8k

Combine like terms: 4k + -8k = -4k
-72 + 18k + 9k2 = 12 + -4k

Solving
-72 + 18k + 9k2 = 12 + -4k

Solving for variable 'k'.

Reorder the terms:
-72 + -12 + 18k + 4k + 9k2 = 12 + -4k + -12 + 4k

Combine like terms: -72 + -12 = -84
-84 + 18k + 4k + 9k2 = 12 + -4k + -12 + 4k

Combine like terms: 18k + 4k = 22k
-84 + 22k + 9k2 = 12 + -4k + -12 + 4k

Reorder the terms:
-84 + 22k + 9k2 = 12 + -12 + -4k + 4k

Combine like terms: 12 + -12 = 0
-84 + 22k + 9k2 = 0 + -4k + 4k
-84 + 22k + 9k2 = -4k + 4k

Combine like terms: -4k + 4k = 0
-84 + 22k + 9k2 = 0

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

Divide each side by '9'.
-9.333333333 + 2.444444444k + k2 = 0

Move the constant term to the right:

Add '9.333333333' to each side of the equation.
-9.333333333 + 2.444444444k + 9.333333333 + k2 = 0 + 9.333333333

Reorder the terms:
-9.333333333 + 9.333333333 + 2.444444444k + k2 = 0 + 9.333333333

Combine like terms: -9.333333333 + 9.333333333 = 0.000000000
0.000000000 + 2.444444444k + k2 = 0 + 9.333333333
2.444444444k + k2 = 0 + 9.333333333

Combine like terms: 0 + 9.333333333 = 9.333333333
2.444444444k + k2 = 9.333333333

The k term is 2.444444444k.  Take half its coefficient (1.222222222).
Square it (1.493827160) and add it to both sides.

Add '1.493827160' to each side of the equation.
2.444444444k + 1.493827160 + k2 = 9.333333333 + 1.493827160

Reorder the terms:
1.493827160 + 2.444444444k + k2 = 9.333333333 + 1.493827160

Combine like terms: 9.333333333 + 1.493827160 = 10.827160493
1.493827160 + 2.444444444k + k2 = 10.827160493

Factor a perfect square on the left side:
(k + 1.222222222)(k + 1.222222222) = 10.827160493

Calculate the square root of the right side: 3.290465088

Break this problem into two subproblems by setting 
(k + 1.222222222) equal to 3.290465088 and -3.290465088.


Subproblem 1
k + 1.222222222 = 3.290465088

Simplifying
k + 1.222222222 = 3.290465088

Reorder the terms:
1.222222222 + k = 3.290465088

Solving
1.222222222 + k = 3.290465088

Solving for variable 'k'.

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

Add '-1.222222222' to each side of the equation.
1.222222222 + -1.222222222 + k = 3.290465088 + -1.222222222

Combine like terms: 1.222222222 + -1.222222222 = 0.000000000
0.000000000 + k = 3.290465088 + -1.222222222
k = 3.290465088 + -1.222222222

Combine like terms: 3.290465088 + -1.222222222 = 2.068242866
k = 2.068242866

Simplifying
k = 2.068242866


Subproblem 2
k + 1.222222222 = -3.290465088

Simplifying
k + 1.222222222 = -3.290465088

Reorder the terms:
1.222222222 + k = -3.290465088

Solving
1.222222222 + k = -3.290465088

Solving for variable 'k'.

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

Add '-1.222222222' to each side of the equation.
1.222222222 + -1.222222222 + k = -3.290465088 + -1.222222222

Combine like terms: 1.222222222 + -1.222222222 = 0.000000000
0.000000000 + k = -3.290465088 + -1.222222222
k = -3.290465088 + -1.222222222

Combine like terms: -3.290465088 + -1.222222222 = -4.51268731
k = -4.51268731

Simplifying
k = -4.51268731


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.068242866, -4.51268731}

See similar equations:

| 2(q-8)=12 | | x+(x+21)=76 | | 24y=-72 | | 7x+24+5x+56=180 | | 5x-8+2x=-3x+2 | | x-(x-21)=76 | | 3(3-v)-6v=15 | | 300x+12200=21000-250x | | -9+n=n-22 | | 8s-22=-16+7s | | 4z-3=3z+4 | | 7x=20x-7 | | x-8*4=5 | | -3x-(-3x+21)=-21 | | 3(x-4)+5=5 | | 25+8x=-15 | | 0.08n=75 | | 4(x-2)=-2+12+5x | | x+21=76 | | 10t+2(t+2)=46 | | 5x+y=84 | | 30=-5d-9 | | 100xy^2+63xy^2= | | 19+x=1999930596 | | 6n-18=4[n+2] | | -1.9(-3x-9)-0.3x= | | 0.5(y-37)=-12 | | 2(1-2)=4y+8 | | -3(-x+2)=2x-6+x | | 3*3*3=27 | | 4h-4=-8 | | 10+8=5y |

Equations solver categories