Solve for M
2m^2 n^2+2mn-12=0
Answers
Answer:
2m2n2 + 2n + -12 = 0
Reorder the terms:
-12 + 2m2n2 + 2n = 0
Solving
-12 + 2m2n2 + 2n = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '12' to each side of the equation.
-12 + 2m2n2 + 12 + 2n = 0 + 12
Reorder the terms:
-12 + 12 + 2m2n2 + 2n = 0 + 12
Combine like terms: -12 + 12 = 0
0 + 2m2n2 + 2n = 0 + 12
2m2n2 + 2n = 0 + 12
Combine like terms: 0 + 12 = 12
2m2n2 + 2n = 12
Add '-2n' to each side of the equation.
2m2n2 + 2n + -2n = 12 + -2n
Combine like terms: 2n + -2n = 0
2m2n2 + 0 = 12 + -2n
2m2n2 = 12 + -2n
Divide each side by '2n2'.
m2 = 6n-2 + -1n-1
Simplifying
m2 = 6n-2 + -1n-1
Reorder the terms:
m2 + -6n-2 + n-1 = 6n-2 + -6n-2 + -1n-1 + n-1
Combine like terms: 6n-2 + -6n-2 = 0
m2 + -6n-2 + n-1 = 0 + -1n-1 + n-1
m2 + -6n-2 + n-1 = -1n-1 + n-1
Combine like terms: -1n-1 + n-1 = 0
m2 + -6n-2 + n-1 = 0
Factor out the Greatest Common Factor (GCF), 'n-2'.
n-2(m2n2 + -6 + n) = 0
Factor a trinomial.
n-2((mn + -2)(mn + 3)) = 0
Subproblem 1
Set the factor 'n-2' equal to zero and attempt to solve:
Simplifying
n-2 = 0
Solving
n-2 = 0
Move all terms containing m to the left, all other terms to the right.
Add '-1n-2' to each side of the equation.
n-2 + -1n-2 = 0 + -1n-2
Remove the zero:
0 = -1n-2
Simplifying
0 = -1n-2
The solution to this equation could not be determined.
This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(mn + -2)' equal to zero and attempt to solve:
Simplifying
mn + -2 = 0
Reorder the terms:
-2 + mn = 0
Solving
-2 + mn = 0
Move all terms containing m to the left, all other terms to the right.
Add '2' to each side of the equation.
-2 + 2 + mn = 0 + 2
Combine like terms: -2 + 2 = 0
0 + mn = 0 + 2
mn = 0 + 2
Combine like terms: 0 + 2 = 2
mn = 2
Divide each side by 'n'.
m = 2n-1
Simplifying
m = 2n-1
Subproblem 3
Set the factor '(mn + 3)' equal to zero and attempt to solve:
Simplifying
mn + 3 = 0
Reorder the terms:
3 + mn = 0
Solving
3 + mn = 0
Move all terms containing m to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + mn = 0 + -3
Combine like terms: 3 + -3 = 0
0 + mn = 0 + -3
mn = 0 + -3
Combine like terms: 0 + -3 = -3
mn = -3
Divide each side by 'n'.
m = -3n-1
Simplifying
m = -3n-1
Solution
m = {2n-1, -3n-1}