4m(m-7)(2m-7)=0

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Solution for 4m(m-7)(2m-7)=0 equation: 


Simplifying
4m(m + -7)(2m + -7) = 0

Reorder the terms:
4m(-7 + m)(2m + -7) = 0

Reorder the terms:
4m(-7 + m)(-7 + 2m) = 0

Multiply (-7 + m) * (-7 + 2m)
4m(-7(-7 + 2m) + m(-7 + 2m)) = 0
4m((-7 * -7 + 2m * -7) + m(-7 + 2m)) = 0
4m((49 + -14m) + m(-7 + 2m)) = 0
4m(49 + -14m + (-7 * m + 2m * m)) = 0
4m(49 + -14m + (-7m + 2m2)) = 0

Combine like terms: -14m + -7m = -21m
4m(49 + -21m + 2m2) = 0
(49 * 4m + -21m * 4m + 2m2 * 4m) = 0
(196m + -84m2 + 8m3) = 0

Solving
196m + -84m2 + 8m3 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4m'.
4m(49 + -21m + 2m2) = 0

Factor a trinomial.
4m((7 + -2m)(7 + -1m)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'm' equal to zero and attempt to solve:

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0

Subproblem 2
Set the factor '(7 + -2m)' equal to zero and attempt to solve:

Simplifying
7 + -2m = 0

Solving
7 + -2m = 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 + -2m = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2m = 0 + -7
-2m = 0 + -7

Combine like terms: 0 + -7 = -7
-2m = -7

Divide each side by '-2'.
m = 3.5

Simplifying
m = 3.5

Subproblem 3
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
Solution
m = {0, 3.5, 7}

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