(5m+12)(m-2)=0

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Solution for (5m+12)(m-2)=0 equation: 


Simplifying
(5m + 12)(m + -2) = 0

Reorder the terms:
(12 + 5m)(m + -2) = 0

Reorder the terms:
(12 + 5m)(-2 + m) = 0

Multiply (12 + 5m) * (-2 + m)
(12(-2 + m) + 5m * (-2 + m)) = 0
((-2 * 12 + m * 12) + 5m * (-2 + m)) = 0
((-24 + 12m) + 5m * (-2 + m)) = 0
(-24 + 12m + (-2 * 5m + m * 5m)) = 0
(-24 + 12m + (-10m + 5m2)) = 0

Combine like terms: 12m + -10m = 2m
(-24 + 2m + 5m2) = 0

Solving
-24 + 2m + 5m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-12 + -5m)(2 + -1m) = 0


Subproblem 1
Set the factor '(-12 + -5m)' equal to zero and attempt to solve:

Simplifying
-12 + -5m = 0

Solving
-12 + -5m = 0

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

Add '12' to each side of the equation.
-12 + 12 + -5m = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -5m = 0 + 12
-5m = 0 + 12

Combine like terms: 0 + 12 = 12
-5m = 12

Divide each side by '-5'.
m = -2.4

Simplifying
m = -2.4

Subproblem 2
Set the factor '(2 + -1m)' equal to zero and attempt to solve:

Simplifying
2 + -1m = 0

Solving
2 + -1m = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1m = 0 + -2
-1m = 0 + -2

Combine like terms: 0 + -2 = -2
-1m = -2

Divide each side by '-1'.
m = 2

Simplifying
m = 2
Solution
m = {-2.4, 2}

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