-5m(3m+6)=-3(4m-2)

Solution for -5m(3m+6)=-3(4m-2) equation:

Simplifying
-5m(3m + 6) = -3(4m + -2)

Reorder the terms:
-5m(6 + 3m) = -3(4m + -2)
(6 * -5m + 3m * -5m) = -3(4m + -2)
(-30m + -15m2) = -3(4m + -2)

Reorder the terms:
-30m + -15m2 = -3(-2 + 4m)
-30m + -15m2 = (-2 * -3 + 4m * -3)
-30m + -15m2 = (6 + -12m)

Solving
-30m + -15m2 = 6 + -12m

Solving for variable 'm'.

Reorder the terms:
-6 + -30m + 12m + -15m2 = 6 + -12m + -6 + 12m

Combine like terms: -30m + 12m = -18m
-6 + -18m + -15m2 = 6 + -12m + -6 + 12m

Reorder the terms:
-6 + -18m + -15m2 = 6 + -6 + -12m + 12m

Combine like terms: 6 + -6 = 0
-6 + -18m + -15m2 = 0 + -12m + 12m
-6 + -18m + -15m2 = -12m + 12m

Combine like terms: -12m + 12m = 0
-6 + -18m + -15m2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(2 + 6m + 5m2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(2 + 6m + 5m2)' equal to zero and attempt to solve:

Simplifying
2 + 6m + 5m2 = 0

Solving
2 + 6m + 5m2 = 0

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

Divide each side by '5'.
0.4 + 1.2m + m2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 1.2m + -0.4 + m2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 1.2m + m2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 1.2m + m2 = 0 + -0.4
1.2m + m2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
1.2m + m2 = -0.4

The m term is 1.2m.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2m + 0.36 + m2 = -0.4 + 0.36

Reorder the terms:
0.36 + 1.2m + m2 = -0.4 + 0.36

Combine like terms: -0.4 + 0.36 = -0.04
0.36 + 1.2m + m2 = -0.04

Factor a perfect square on the left side:
(m + 0.6)(m + 0.6) = -0.04

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.