52m^2-13m-48m+12=150

Solution for 52m^2-13m-48m+12=150 equation:

Simplifying
52m2 + -13m + -48m + 12 = 150

Reorder the terms:
12 + -13m + -48m + 52m2 = 150

Combine like terms: -13m + -48m = -61m
12 + -61m + 52m2 = 150

Solving
12 + -61m + 52m2 = 150

Solving for variable 'm'.

Reorder the terms:
12 + -150 + -61m + 52m2 = 150 + -150

Combine like terms: 12 + -150 = -138
-138 + -61m + 52m2 = 150 + -150

Combine like terms: 150 + -150 = 0
-138 + -61m + 52m2 = 0

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

Divide each side by '52'.
-2.653846154 + -1.173076923m + m2 = 0

Move the constant term to the right:

Add '2.653846154' to each side of the equation.
-2.653846154 + -1.173076923m + 2.653846154 + m2 = 0 + 2.653846154

Reorder the terms:
-2.653846154 + 2.653846154 + -1.173076923m + m2 = 0 + 2.653846154

Combine like terms: -2.653846154 + 2.653846154 = 0.000000000
0.000000000 + -1.173076923m + m2 = 0 + 2.653846154
-1.173076923m + m2 = 0 + 2.653846154

Combine like terms: 0 + 2.653846154 = 2.653846154
-1.173076923m + m2 = 2.653846154

The m term is -1.173076923m.  Take half its coefficient (-0.5865384615).
Square it (0.3440273668) and add it to both sides.

Add '0.3440273668' to each side of the equation.
-1.173076923m + 0.3440273668 + m2 = 2.653846154 + 0.3440273668

Reorder the terms:
0.3440273668 + -1.173076923m + m2 = 2.653846154 + 0.3440273668

Combine like terms: 2.653846154 + 0.3440273668 = 2.9978735208
0.3440273668 + -1.173076923m + m2 = 2.9978735208

Factor a perfect square on the left side:
(m + -0.5865384615)(m + -0.5865384615) = 2.9978735208

Calculate the square root of the right side: 1.731436837

Break this problem into two subproblems by setting 
(m + -0.5865384615) equal to 1.731436837 and -1.731436837.

Subproblem 1
m + -0.5865384615 = 1.731436837

Simplifying
m + -0.5865384615 = 1.731436837

Reorder the terms:
-0.5865384615 + m = 1.731436837

Solving
-0.5865384615 + m = 1.731436837

Solving for variable 'm'.

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

Add '0.5865384615' to each side of the equation.
-0.5865384615 + 0.5865384615 + m = 1.731436837 + 0.5865384615

Combine like terms: -0.5865384615 + 0.5865384615 = 0.0000000000
0.0000000000 + m = 1.731436837 + 0.5865384615
m = 1.731436837 + 0.5865384615

Combine like terms: 1.731436837 + 0.5865384615 = 2.3179752985
m = 2.3179752985

Simplifying
m = 2.3179752985

Subproblem 2
m + -0.5865384615 = -1.731436837

Simplifying
m + -0.5865384615 = -1.731436837

Reorder the terms:
-0.5865384615 + m = -1.731436837

Solving
-0.5865384615 + m = -1.731436837

Solving for variable 'm'.

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

Add '0.5865384615' to each side of the equation.
-0.5865384615 + 0.5865384615 + m = -1.731436837 + 0.5865384615

Combine like terms: -0.5865384615 + 0.5865384615 = 0.0000000000
0.0000000000 + m = -1.731436837 + 0.5865384615
m = -1.731436837 + 0.5865384615

Combine like terms: -1.731436837 + 0.5865384615 = -1.1448983755
m = -1.1448983755

Simplifying
m = -1.1448983755

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.3179752985, -1.1448983755}