12m^2+50m-42=0

Solution for 12m^2+50m-42=0 equation:

Simplifying
12m2 + 50m + -42 = 0

Reorder the terms:
-42 + 50m + 12m2 = 0

Solving
-42 + 50m + 12m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 25m + 6m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + 25m + 6m2)' equal to zero and attempt to solve:

Simplifying
-21 + 25m + 6m2 = 0

Solving
-21 + 25m + 6m2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-3.5 + 4.166666667m + m2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 4.166666667m + 3.5 + m2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 4.166666667m + m2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 4.166666667m + m2 = 0 + 3.5
4.166666667m + m2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
4.166666667m + m2 = 3.5

The m term is 4.166666667m.  Take half its coefficient (2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
4.166666667m + 4.340277781 + m2 = 3.5 + 4.340277781

Reorder the terms:
4.340277781 + 4.166666667m + m2 = 3.5 + 4.340277781

Combine like terms: 3.5 + 4.340277781 = 7.840277781
4.340277781 + 4.166666667m + m2 = 7.840277781

Factor a perfect square on the left side:
(m + 2.083333334)(m + 2.083333334) = 7.840277781

Calculate the square root of the right side: 2.800049603

Break this problem into two subproblems by setting 
(m + 2.083333334) equal to 2.800049603 and -2.800049603.

Subproblem 1
m + 2.083333334 = 2.800049603

Simplifying
m + 2.083333334 = 2.800049603

Reorder the terms:
2.083333334 + m = 2.800049603

Solving
2.083333334 + m = 2.800049603

Solving for variable 'm'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + m = 2.800049603 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + m = 2.800049603 + -2.083333334
m = 2.800049603 + -2.083333334

Combine like terms: 2.800049603 + -2.083333334 = 0.716716269
m = 0.716716269

Simplifying
m = 0.716716269

Subproblem 2
m + 2.083333334 = -2.800049603

Simplifying
m + 2.083333334 = -2.800049603

Reorder the terms:
2.083333334 + m = -2.800049603

Solving
2.083333334 + m = -2.800049603

Solving for variable 'm'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + m = -2.800049603 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + m = -2.800049603 + -2.083333334
m = -2.800049603 + -2.083333334

Combine like terms: -2.800049603 + -2.083333334 = -4.883382937
m = -4.883382937

Simplifying
m = -4.883382937

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.716716269, -4.883382937}
Solution
m = {0.716716269, -4.883382937}