16m^2-6=-15+30m-8m^2

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Solution for 16m^2-6=-15+30m-8m^2 equation: 


Simplifying
16m2 + -6 = -15 + 30m + -8m2

Reorder the terms:
-6 + 16m2 = -15 + 30m + -8m2

Solving
-6 + 16m2 = -15 + 30m + -8m2

Solving for variable 'm'.

Reorder the terms:
-6 + 15 + -30m + 16m2 + 8m2 = -15 + 30m + -8m2 + 15 + -30m + 8m2

Combine like terms: -6 + 15 = 9
9 + -30m + 16m2 + 8m2 = -15 + 30m + -8m2 + 15 + -30m + 8m2

Combine like terms: 16m2 + 8m2 = 24m2
9 + -30m + 24m2 = -15 + 30m + -8m2 + 15 + -30m + 8m2

Reorder the terms:
9 + -30m + 24m2 = -15 + 15 + 30m + -30m + -8m2 + 8m2

Combine like terms: -15 + 15 = 0
9 + -30m + 24m2 = 0 + 30m + -30m + -8m2 + 8m2
9 + -30m + 24m2 = 30m + -30m + -8m2 + 8m2

Combine like terms: 30m + -30m = 0
9 + -30m + 24m2 = 0 + -8m2 + 8m2
9 + -30m + 24m2 = -8m2 + 8m2

Combine like terms: -8m2 + 8m2 = 0
9 + -30m + 24m2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -10m + 8m2) = 0

Factor a trinomial.
3((1 + -2m)(3 + -4m)) = 0

Ignore the factor 3.

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

Simplifying
1 + -2m = 0

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

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

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

Divide each side by '-2'.
m = 0.5

Simplifying
m = 0.5

Subproblem 2
Set the factor '(3 + -4m)' equal to zero and attempt to solve:

Simplifying
3 + -4m = 0

Solving
3 + -4m = 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 + -4m = 0 + -3

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

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

Divide each side by '-4'.
m = 0.75

Simplifying
m = 0.75
Solution
m = {0.5, 0.75}

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