8m^2+5m-21=-9m+m^2

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Solution for 8m^2+5m-21=-9m+m^2 equation: 


Simplifying
8m2 + 5m + -21 = -9m + m2

Reorder the terms:
-21 + 5m + 8m2 = -9m + m2

Solving
-21 + 5m + 8m2 = -9m + m2

Solving for variable 'm'.

Reorder the terms:
-21 + 5m + 9m + 8m2 + -1m2 = -9m + m2 + 9m + -1m2

Combine like terms: 5m + 9m = 14m
-21 + 14m + 8m2 + -1m2 = -9m + m2 + 9m + -1m2

Combine like terms: 8m2 + -1m2 = 7m2
-21 + 14m + 7m2 = -9m + m2 + 9m + -1m2

Reorder the terms:
-21 + 14m + 7m2 = -9m + 9m + m2 + -1m2

Combine like terms: -9m + 9m = 0
-21 + 14m + 7m2 = 0 + m2 + -1m2
-21 + 14m + 7m2 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
-21 + 14m + 7m2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + 2m + m2) = 0

Factor a trinomial.
7((-3 + -1m)(1 + -1m)) = 0

Ignore the factor 7.

Subproblem 1
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

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

Simplifying
1 + -1m = 0

Solving
1 + -1m = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1m = 0 + -1

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

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

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

Simplifying
m = 1
Solution
m = {-3, 1}

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