7(m-5)(m-2)=0

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Solution for 7(m-5)(m-2)=0 equation: 


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

Reorder the terms:
7(-5 + m)(m + -2) = 0

Reorder the terms:
7(-5 + m)(-2 + m) = 0

Multiply (-5 + m) * (-2 + m)
7(-5(-2 + m) + m(-2 + m)) = 0
7((-2 * -5 + m * -5) + m(-2 + m)) = 0
7((10 + -5m) + m(-2 + m)) = 0
7(10 + -5m + (-2 * m + m * m)) = 0
7(10 + -5m + (-2m + m2)) = 0

Combine like terms: -5m + -2m = -7m
7(10 + -7m + m2) = 0
(10 * 7 + -7m * 7 + m2 * 7) = 0
(70 + -49m + 7m2) = 0

Solving
70 + -49m + 7m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '7'.
7(10 + -7m + m2) = 0

Factor a trinomial.
7((2 + -1m)(5 + -1m)) = 0

Ignore the factor 7.

Subproblem 1
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

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

Simplifying
5 + -1m = 0

Solving
5 + -1m = 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 + -1m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1m = 0 + -5
-1m = 0 + -5

Combine like terms: 0 + -5 = -5
-1m = -5

Divide each side by '-1'.
m = 5

Simplifying
m = 5
Solution
m = {2, 5}

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