(2m+4)(2m-8)=(5m-2)(2m+4)

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Solution for (2m+4)(2m-8)=(5m-2)(2m+4) equation: 


Simplifying
(2m + 4)(2m + -8) = (5m + -2)(2m + 4)

Reorder the terms:
(4 + 2m)(2m + -8) = (5m + -2)(2m + 4)

Reorder the terms:
(4 + 2m)(-8 + 2m) = (5m + -2)(2m + 4)

Multiply (4 + 2m) * (-8 + 2m)
(4(-8 + 2m) + 2m * (-8 + 2m)) = (5m + -2)(2m + 4)
((-8 * 4 + 2m * 4) + 2m * (-8 + 2m)) = (5m + -2)(2m + 4)
((-32 + 8m) + 2m * (-8 + 2m)) = (5m + -2)(2m + 4)
(-32 + 8m + (-8 * 2m + 2m * 2m)) = (5m + -2)(2m + 4)
(-32 + 8m + (-16m + 4m2)) = (5m + -2)(2m + 4)

Combine like terms: 8m + -16m = -8m
(-32 + -8m + 4m2) = (5m + -2)(2m + 4)

Reorder the terms:
-32 + -8m + 4m2 = (-2 + 5m)(2m + 4)

Reorder the terms:
-32 + -8m + 4m2 = (-2 + 5m)(4 + 2m)

Multiply (-2 + 5m) * (4 + 2m)
-32 + -8m + 4m2 = (-2(4 + 2m) + 5m * (4 + 2m))
-32 + -8m + 4m2 = ((4 * -2 + 2m * -2) + 5m * (4 + 2m))
-32 + -8m + 4m2 = ((-8 + -4m) + 5m * (4 + 2m))
-32 + -8m + 4m2 = (-8 + -4m + (4 * 5m + 2m * 5m))
-32 + -8m + 4m2 = (-8 + -4m + (20m + 10m2))

Combine like terms: -4m + 20m = 16m
-32 + -8m + 4m2 = (-8 + 16m + 10m2)

Solving
-32 + -8m + 4m2 = -8 + 16m + 10m2

Solving for variable 'm'.

Reorder the terms:
-32 + 8 + -8m + -16m + 4m2 + -10m2 = -8 + 16m + 10m2 + 8 + -16m + -10m2

Combine like terms: -32 + 8 = -24
-24 + -8m + -16m + 4m2 + -10m2 = -8 + 16m + 10m2 + 8 + -16m + -10m2

Combine like terms: -8m + -16m = -24m
-24 + -24m + 4m2 + -10m2 = -8 + 16m + 10m2 + 8 + -16m + -10m2

Combine like terms: 4m2 + -10m2 = -6m2
-24 + -24m + -6m2 = -8 + 16m + 10m2 + 8 + -16m + -10m2

Reorder the terms:
-24 + -24m + -6m2 = -8 + 8 + 16m + -16m + 10m2 + -10m2

Combine like terms: -8 + 8 = 0
-24 + -24m + -6m2 = 0 + 16m + -16m + 10m2 + -10m2
-24 + -24m + -6m2 = 16m + -16m + 10m2 + -10m2

Combine like terms: 16m + -16m = 0
-24 + -24m + -6m2 = 0 + 10m2 + -10m2
-24 + -24m + -6m2 = 10m2 + -10m2

Combine like terms: 10m2 + -10m2 = 0
-24 + -24m + -6m2 = 0

Factor out the Greatest Common Factor (GCF), '-6'.
-6(4 + 4m + m2) = 0

Factor a trinomial.
-6((2 + m)(2 + m)) = 0

Ignore the factor -6.

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

Simplifying
2 + m = 0

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

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

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

Simplifying
m = -2

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

Simplifying
2 + m = 0

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

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

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

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

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