(5m-4)(7m+8)=0

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Solution for (5m-4)(7m+8)=0 equation: 


Simplifying
(5m + -4)(7m + 8) = 0

Reorder the terms:
(-4 + 5m)(7m + 8) = 0

Reorder the terms:
(-4 + 5m)(8 + 7m) = 0

Multiply (-4 + 5m) * (8 + 7m)
(-4(8 + 7m) + 5m * (8 + 7m)) = 0
((8 * -4 + 7m * -4) + 5m * (8 + 7m)) = 0
((-32 + -28m) + 5m * (8 + 7m)) = 0
(-32 + -28m + (8 * 5m + 7m * 5m)) = 0
(-32 + -28m + (40m + 35m2)) = 0

Combine like terms: -28m + 40m = 12m
(-32 + 12m + 35m2) = 0

Solving
-32 + 12m + 35m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-8 + -7m)(4 + -5m) = 0


Subproblem 1
Set the factor '(-8 + -7m)' equal to zero and attempt to solve:

Simplifying
-8 + -7m = 0

Solving
-8 + -7m = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7m = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7m = 0 + 8
-7m = 0 + 8

Combine like terms: 0 + 8 = 8
-7m = 8

Divide each side by '-7'.
m = -1.142857143

Simplifying
m = -1.142857143

Subproblem 2
Set the factor '(4 + -5m)' equal to zero and attempt to solve:

Simplifying
4 + -5m = 0

Solving
4 + -5m = 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 + -5m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5m = 0 + -4
-5m = 0 + -4

Combine like terms: 0 + -4 = -4
-5m = -4

Divide each side by '-5'.
m = 0.8

Simplifying
m = 0.8
Solution
m = {-1.142857143, 0.8}

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