(m+15-30)2*m-20=

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Solution for (m+15-30)2*m-20= equation:


Simplifying
(m + 15 + -30) * 2m + -20 = 0

Reorder the terms:
(15 + -30 + m) * 2m + -20 = 0

Combine like terms: 15 + -30 = -15
(-15 + m) * 2m + -20 = 0

Reorder the terms for easier multiplication:
2m(-15 + m) + -20 = 0
(-15 * 2m + m * 2m) + -20 = 0
(-30m + 2m2) + -20 = 0

Reorder the terms:
-20 + -30m + 2m2 = 0

Solving
-20 + -30m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -15m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + -15m + m2)' equal to zero and attempt to solve:

Simplifying
-10 + -15m + m2 = 0

Solving
-10 + -15m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -15m + 10 + m2 = 0 + 10

Reorder the terms:
-10 + 10 + -15m + m2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -15m + m2 = 0 + 10
-15m + m2 = 0 + 10

Combine like terms: 0 + 10 = 10
-15m + m2 = 10

The m term is -15m.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15m + 56.25 + m2 = 10 + 56.25

Reorder the terms:
56.25 + -15m + m2 = 10 + 56.25

Combine like terms: 10 + 56.25 = 66.25
56.25 + -15m + m2 = 66.25

Factor a perfect square on the left side:
(m + -7.5)(m + -7.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(m + -7.5) equal to 8.139410298 and -8.139410298.


Subproblem 1
m + -7.5 = 8.139410298

Simplifying
m + -7.5 = 8.139410298

Reorder the terms:
-7.5 + m = 8.139410298

Solving
-7.5 + m = 8.139410298

Solving for variable 'm'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + m = 8.139410298 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + m = 8.139410298 + 7.5
m = 8.139410298 + 7.5

Combine like terms: 8.139410298 + 7.5 = 15.639410298
m = 15.639410298

Simplifying
m = 15.639410298


Subproblem 2
m + -7.5 = -8.139410298

Simplifying
m + -7.5 = -8.139410298

Reorder the terms:
-7.5 + m = -8.139410298

Solving
-7.5 + m = -8.139410298

Solving for variable 'm'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + m = -8.139410298 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + m = -8.139410298 + 7.5
m = -8.139410298 + 7.5

Combine like terms: -8.139410298 + 7.5 = -0.639410298
m = -0.639410298

Simplifying
m = -0.639410298


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {15.639410298, -0.639410298}
Solution
m = {15.639410298, -0.639410298}

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