2m^2-8m=2m-12

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Solution for 2m^2-8m=2m-12 equation:


Simplifying
2m2 + -8m = 2m + -12

Reorder the terms:
-8m + 2m2 = 2m + -12

Reorder the terms:
-8m + 2m2 = -12 + 2m

Solving
-8m + 2m2 = -12 + 2m

Solving for variable 'm'.

Reorder the terms:
12 + -8m + -2m + 2m2 = -12 + 2m + 12 + -2m

Combine like terms: -8m + -2m = -10m
12 + -10m + 2m2 = -12 + 2m + 12 + -2m

Reorder the terms:
12 + -10m + 2m2 = -12 + 12 + 2m + -2m

Combine like terms: -12 + 12 = 0
12 + -10m + 2m2 = 0 + 2m + -2m
12 + -10m + 2m2 = 2m + -2m

Combine like terms: 2m + -2m = 0
12 + -10m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -5m + m2) = 0

Factor a trinomial.
2((2 + -1m)(3 + -1m)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -1m)' equal to zero and attempt to solve:

Simplifying
2 + -1m = 0

Solving
2 + -1m = 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 + -1m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1m = 0 + -2
-1m = 0 + -2

Combine like terms: 0 + -2 = -2
-1m = -2

Divide each side by '-1'.
m = 2

Simplifying
m = 2

Subproblem 2
Set the factor '(3 + -1m)' equal to zero and attempt to solve:

Simplifying
3 + -1m = 0

Solving
3 + -1m = 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 + -1m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1m = 0 + -3
-1m = 0 + -3

Combine like terms: 0 + -3 = -3
-1m = -3

Divide each side by '-1'.
m = 3

Simplifying
m = 3
Solution
m = {2, 3}

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