42+32m=-4m^2+6m

Solution for 42+32m=-4m^2+6m equation:

Simplifying
42 + 32m = -4m2 + 6m

Reorder the terms:
42 + 32m = 6m + -4m2

Solving
42 + 32m = 6m + -4m2

Solving for variable 'm'.

Combine like terms: 32m + -6m = 26m
42 + 26m + 4m2 = 6m + -4m2 + -6m + 4m2

Reorder the terms:
42 + 26m + 4m2 = 6m + -6m + -4m2 + 4m2

Combine like terms: 6m + -6m = 0
42 + 26m + 4m2 = 0 + -4m2 + 4m2
42 + 26m + 4m2 = -4m2 + 4m2

Combine like terms: -4m2 + 4m2 = 0
42 + 26m + 4m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 13m + 2m2) = 0

Factor a trinomial.
2((7 + 2m)(3 + m)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + 2m)' equal to zero and attempt to solve:

Simplifying
7 + 2m = 0

Solving
7 + 2m = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2m = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2m = 0 + -7
2m = 0 + -7

Combine like terms: 0 + -7 = -7
2m = -7

Divide each side by '2'.
m = -3.5

Simplifying
m = -3.5
Subproblem 2
Set the factor '(3 + m)' equal to zero and attempt to solve:

Simplifying
3 + m = 0

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

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

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

Simplifying
m = -3
Solution
m = {-3.5, -3}