5(3m-5)(m+7)=0

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Solution for 5(3m-5)(m+7)=0 equation: 


Simplifying
5(3m + -5)(m + 7) = 0

Reorder the terms:
5(-5 + 3m)(m + 7) = 0

Reorder the terms:
5(-5 + 3m)(7 + m) = 0

Multiply (-5 + 3m) * (7 + m)
5(-5(7 + m) + 3m * (7 + m)) = 0
5((7 * -5 + m * -5) + 3m * (7 + m)) = 0
5((-35 + -5m) + 3m * (7 + m)) = 0
5(-35 + -5m + (7 * 3m + m * 3m)) = 0
5(-35 + -5m + (21m + 3m2)) = 0

Combine like terms: -5m + 21m = 16m
5(-35 + 16m + 3m2) = 0
(-35 * 5 + 16m * 5 + 3m2 * 5) = 0
(-175 + 80m + 15m2) = 0

Solving
-175 + 80m + 15m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-35 + 16m + 3m2) = 0

Factor a trinomial.
5((-7 + -1m)(5 + -3m)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -1m)' equal to zero and attempt to solve:

Simplifying
-7 + -1m = 0

Solving
-7 + -1m = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1m = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1m = 0 + 7
-1m = 0 + 7

Combine like terms: 0 + 7 = 7
-1m = 7

Divide each side by '-1'.
m = -7

Simplifying
m = -7

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

Simplifying
5 + -3m = 0

Solving
5 + -3m = 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 + -3m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3m = 0 + -5
-3m = 0 + -5

Combine like terms: 0 + -5 = -5
-3m = -5

Divide each side by '-3'.
m = 1.666666667

Simplifying
m = 1.666666667
Solution
m = {-7, 1.666666667}

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