12+m(m+1)=-2+4(m+6)

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Solution for 12+m(m+1)=-2+4(m+6) equation: 


Simplifying
12 + m(m + 1) = -2 + 4(m + 6)

Reorder the terms:
12 + m(1 + m) = -2 + 4(m + 6)
12 + (1 * m + m * m) = -2 + 4(m + 6)
12 + (1m + m2) = -2 + 4(m + 6)

Reorder the terms:
12 + 1m + m2 = -2 + 4(6 + m)
12 + 1m + m2 = -2 + (6 * 4 + m * 4)
12 + 1m + m2 = -2 + (24 + 4m)

Combine like terms: -2 + 24 = 22
12 + 1m + m2 = 22 + 4m

Solving
12 + 1m + m2 = 22 + 4m

Solving for variable 'm'.

Reorder the terms:
12 + -22 + 1m + -4m + m2 = 22 + 4m + -22 + -4m

Combine like terms: 12 + -22 = -10
-10 + 1m + -4m + m2 = 22 + 4m + -22 + -4m

Combine like terms: 1m + -4m = -3m
-10 + -3m + m2 = 22 + 4m + -22 + -4m

Reorder the terms:
-10 + -3m + m2 = 22 + -22 + 4m + -4m

Combine like terms: 22 + -22 = 0
-10 + -3m + m2 = 0 + 4m + -4m
-10 + -3m + m2 = 4m + -4m

Combine like terms: 4m + -4m = 0
-10 + -3m + m2 = 0

Factor a trinomial.
(-2 + -1m)(5 + -1m) = 0


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 '(5 + -1m)' equal to zero and attempt to solve:

Simplifying
5 + -1m = 0

Solving
5 + -1m = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1m = 0 + -5
-1m = 0 + -5

Combine like terms: 0 + -5 = -5
-1m = -5

Divide each side by '-1'.
m = 5

Simplifying
m = 5
Solution
m = {-2, 5}

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