3m(m-10)=90

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Solution for 3m(m-10)=90 equation: 


Simplifying
3m(m + -10) = 90

Reorder the terms:
3m(-10 + m) = 90
(-10 * 3m + m * 3m) = 90
(-30m + 3m2) = 90

Solving
-30m + 3m2 = 90

Solving for variable 'm'.

Reorder the terms:
-90 + -30m + 3m2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -30m + 3m2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + -10m + m2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-30 + -10m + m2)' equal to zero and attempt to solve:

Simplifying
-30 + -10m + m2 = 0

Solving
-30 + -10m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -10m + 30 + m2 = 0 + 30

Reorder the terms:
-30 + 30 + -10m + m2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -10m + m2 = 0 + 30
-10m + m2 = 0 + 30

Combine like terms: 0 + 30 = 30
-10m + m2 = 30

The m term is -10m.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10m + 25 + m2 = 30 + 25

Reorder the terms:
25 + -10m + m2 = 30 + 25

Combine like terms: 30 + 25 = 55
25 + -10m + m2 = 55

Factor a perfect square on the left side:
(m + -5)(m + -5) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(m + -5) equal to 7.416198487 and -7.416198487.


Subproblem 1
m + -5 = 7.416198487

Simplifying
m + -5 = 7.416198487

Reorder the terms:
-5 + m = 7.416198487

Solving
-5 + m = 7.416198487

Solving for variable 'm'.

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

Add '5' to each side of the equation.
-5 + 5 + m = 7.416198487 + 5

Combine like terms: -5 + 5 = 0
0 + m = 7.416198487 + 5
m = 7.416198487 + 5

Combine like terms: 7.416198487 + 5 = 12.416198487
m = 12.416198487

Simplifying
m = 12.416198487


Subproblem 2
m + -5 = -7.416198487

Simplifying
m + -5 = -7.416198487

Reorder the terms:
-5 + m = -7.416198487

Solving
-5 + m = -7.416198487

Solving for variable 'm'.

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

Add '5' to each side of the equation.
-5 + 5 + m = -7.416198487 + 5

Combine like terms: -5 + 5 = 0
0 + m = -7.416198487 + 5
m = -7.416198487 + 5

Combine like terms: -7.416198487 + 5 = -2.416198487
m = -2.416198487

Simplifying
m = -2.416198487


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {12.416198487, -2.416198487}
Solution
m = {12.416198487, -2.416198487}

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