3(m-9)2(m+3)=-6

Solution for 3(m-9)2(m+3)=-6 equation:

Simplifying
3(m + -9) * 2(m + 3) = -6

Reorder the terms:
3(-9 + m) * 2(m + 3) = -6

Reorder the terms:
3(-9 + m) * 2(3 + m) = -6

Reorder the terms for easier multiplication:
3 * 2(-9 + m)(3 + m) = -6

Multiply 3 * 2
6(-9 + m)(3 + m) = -6

Multiply (-9 + m) * (3 + m)
6(-9(3 + m) + m(3 + m)) = -6
6((3 * -9 + m * -9) + m(3 + m)) = -6
6((-27 + -9m) + m(3 + m)) = -6
6(-27 + -9m + (3 * m + m * m)) = -6
6(-27 + -9m + (3m + m2)) = -6

Combine like terms: -9m + 3m = -6m
6(-27 + -6m + m2) = -6
(-27 * 6 + -6m * 6 + m2 * 6) = -6
(-162 + -36m + 6m2) = -6

Solving
-162 + -36m + 6m2 = -6

Solving for variable 'm'.

Reorder the terms:
-162 + 6 + -36m + 6m2 = -6 + 6

Combine like terms: -162 + 6 = -156
-156 + -36m + 6m2 = -6 + 6

Combine like terms: -6 + 6 = 0
-156 + -36m + 6m2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-26 + -6m + m2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-26 + -6m + m2)' equal to zero and attempt to solve:

Simplifying
-26 + -6m + m2 = 0

Solving
-26 + -6m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -6m + 26 + m2 = 0 + 26

Reorder the terms:
-26 + 26 + -6m + m2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -6m + m2 = 0 + 26
-6m + m2 = 0 + 26

Combine like terms: 0 + 26 = 26
-6m + m2 = 26

The m term is -6m.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6m + 9 + m2 = 26 + 9

Reorder the terms:
9 + -6m + m2 = 26 + 9

Combine like terms: 26 + 9 = 35
9 + -6m + m2 = 35

Factor a perfect square on the left side:
(m + -3)(m + -3) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(m + -3) equal to 5.916079783 and -5.916079783.

Subproblem 1
m + -3 = 5.916079783

Simplifying
m + -3 = 5.916079783

Reorder the terms:
-3 + m = 5.916079783

Solving
-3 + m = 5.916079783

Solving for variable 'm'.

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

Add '3' to each side of the equation.
-3 + 3 + m = 5.916079783 + 3

Combine like terms: -3 + 3 = 0
0 + m = 5.916079783 + 3
m = 5.916079783 + 3

Combine like terms: 5.916079783 + 3 = 8.916079783
m = 8.916079783

Simplifying
m = 8.916079783

Subproblem 2
m + -3 = -5.916079783

Simplifying
m + -3 = -5.916079783

Reorder the terms:
-3 + m = -5.916079783

Solving
-3 + m = -5.916079783

Solving for variable 'm'.

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

Add '3' to each side of the equation.
-3 + 3 + m = -5.916079783 + 3

Combine like terms: -3 + 3 = 0
0 + m = -5.916079783 + 3
m = -5.916079783 + 3

Combine like terms: -5.916079783 + 3 = -2.916079783
m = -2.916079783

Simplifying
m = -2.916079783

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {8.916079783, -2.916079783}
Solution
m = {8.916079783, -2.916079783}