(3m+4)(m-5m+8)=0

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Solution for (3m+4)(m-5m+8)=0 equation: 


Simplifying
(3m + 4)(m + -5m + 8) = 0

Reorder the terms:
(4 + 3m)(m + -5m + 8) = 0

Reorder the terms:
(4 + 3m)(8 + m + -5m) = 0

Combine like terms: m + -5m = -4m
(4 + 3m)(8 + -4m) = 0

Multiply (4 + 3m) * (8 + -4m)
(4(8 + -4m) + 3m * (8 + -4m)) = 0
((8 * 4 + -4m * 4) + 3m * (8 + -4m)) = 0
((32 + -16m) + 3m * (8 + -4m)) = 0
(32 + -16m + (8 * 3m + -4m * 3m)) = 0
(32 + -16m + (24m + -12m2)) = 0

Combine like terms: -16m + 24m = 8m
(32 + 8m + -12m2) = 0

Solving
32 + 8m + -12m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 2m + -3m2) = 0

Factor a trinomial.
4((2 + -1m)(4 + 3m)) = 0

Ignore the factor 4.

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 '(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, -1.333333333}

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