5(m-2)=3m(2m+6)

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Solution for 5(m-2)=3m(2m+6) equation: 


Simplifying
5(m + -2) = 3m(2m + 6)

Reorder the terms:
5(-2 + m) = 3m(2m + 6)
(-2 * 5 + m * 5) = 3m(2m + 6)
(-10 + 5m) = 3m(2m + 6)

Reorder the terms:
-10 + 5m = 3m(6 + 2m)
-10 + 5m = (6 * 3m + 2m * 3m)
-10 + 5m = (18m + 6m2)

Solving
-10 + 5m = 18m + 6m2

Solving for variable 'm'.

Combine like terms: 5m + -18m = -13m
-10 + -13m + -6m2 = 18m + 6m2 + -18m + -6m2

Reorder the terms:
-10 + -13m + -6m2 = 18m + -18m + 6m2 + -6m2

Combine like terms: 18m + -18m = 0
-10 + -13m + -6m2 = 0 + 6m2 + -6m2
-10 + -13m + -6m2 = 6m2 + -6m2

Combine like terms: 6m2 + -6m2 = 0
-10 + -13m + -6m2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 13m + 6m2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(10 + 13m + 6m2)' equal to zero and attempt to solve:

Simplifying
10 + 13m + 6m2 = 0

Solving
10 + 13m + 6m2 = 0

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

Divide each side by '6'.
1.666666667 + 2.166666667m + m2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 2.166666667m + -1.666666667 + m2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 2.166666667m + m2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 2.166666667m + m2 = 0 + -1.666666667
2.166666667m + m2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
2.166666667m + m2 = -1.666666667

The m term is 2.166666667m.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667m + 1.173611113 + m2 = -1.666666667 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667m + m2 = -1.666666667 + 1.173611113

Combine like terms: -1.666666667 + 1.173611113 = -0.493055554
1.173611113 + 2.166666667m + m2 = -0.493055554

Factor a perfect square on the left side:
(m + 1.083333334)(m + 1.083333334) = -0.493055554

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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