5(3m-4)(2m+5)=0

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Solution for 5(3m-4)(2m+5)=0 equation: 


Simplifying
5(3m + -4)(2m + 5) = 0

Reorder the terms:
5(-4 + 3m)(2m + 5) = 0

Reorder the terms:
5(-4 + 3m)(5 + 2m) = 0

Multiply (-4 + 3m) * (5 + 2m)
5(-4(5 + 2m) + 3m * (5 + 2m)) = 0
5((5 * -4 + 2m * -4) + 3m * (5 + 2m)) = 0
5((-20 + -8m) + 3m * (5 + 2m)) = 0
5(-20 + -8m + (5 * 3m + 2m * 3m)) = 0
5(-20 + -8m + (15m + 6m2)) = 0

Combine like terms: -8m + 15m = 7m
5(-20 + 7m + 6m2) = 0
(-20 * 5 + 7m * 5 + 6m2 * 5) = 0
(-100 + 35m + 30m2) = 0

Solving
-100 + 35m + 30m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + 7m + 6m2) = 0

Factor a trinomial.
5((-5 + -2m)(4 + -3m)) = 0

Ignore the factor 5.

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

Simplifying
-5 + -2m = 0

Solving
-5 + -2m = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2m = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2m = 0 + 5
-2m = 0 + 5

Combine like terms: 0 + 5 = 5
-2m = 5

Divide each side by '-2'.
m = -2.5

Simplifying
m = -2.5

Subproblem 2
Set the factor '(4 + -3m)' equal to zero and attempt to solve:

Simplifying
4 + -3m = 0

Solving
4 + -3m = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3m = 0 + -4
-3m = 0 + -4

Combine like terms: 0 + -4 = -4
-3m = -4

Divide each side by '-3'.
m = 1.333333333

Simplifying
m = 1.333333333
Solution
m = {-2.5, 1.333333333}

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