(2m-5)(3m+6)=(6m-5)(m+4)

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Solution for (2m-5)(3m+6)=(6m-5)(m+4) equation: 


Simplifying
(2m + -5)(3m + 6) = (6m + -5)(m + 4)

Reorder the terms:
(-5 + 2m)(3m + 6) = (6m + -5)(m + 4)

Reorder the terms:
(-5 + 2m)(6 + 3m) = (6m + -5)(m + 4)

Multiply (-5 + 2m) * (6 + 3m)
(-5(6 + 3m) + 2m * (6 + 3m)) = (6m + -5)(m + 4)
((6 * -5 + 3m * -5) + 2m * (6 + 3m)) = (6m + -5)(m + 4)
((-30 + -15m) + 2m * (6 + 3m)) = (6m + -5)(m + 4)
(-30 + -15m + (6 * 2m + 3m * 2m)) = (6m + -5)(m + 4)
(-30 + -15m + (12m + 6m2)) = (6m + -5)(m + 4)

Combine like terms: -15m + 12m = -3m
(-30 + -3m + 6m2) = (6m + -5)(m + 4)

Reorder the terms:
-30 + -3m + 6m2 = (-5 + 6m)(m + 4)

Reorder the terms:
-30 + -3m + 6m2 = (-5 + 6m)(4 + m)

Multiply (-5 + 6m) * (4 + m)
-30 + -3m + 6m2 = (-5(4 + m) + 6m * (4 + m))
-30 + -3m + 6m2 = ((4 * -5 + m * -5) + 6m * (4 + m))
-30 + -3m + 6m2 = ((-20 + -5m) + 6m * (4 + m))
-30 + -3m + 6m2 = (-20 + -5m + (4 * 6m + m * 6m))
-30 + -3m + 6m2 = (-20 + -5m + (24m + 6m2))

Combine like terms: -5m + 24m = 19m
-30 + -3m + 6m2 = (-20 + 19m + 6m2)

Add '-6m2' to each side of the equation.
-30 + -3m + 6m2 + -6m2 = -20 + 19m + 6m2 + -6m2

Combine like terms: 6m2 + -6m2 = 0
-30 + -3m + 0 = -20 + 19m + 6m2 + -6m2
-30 + -3m = -20 + 19m + 6m2 + -6m2

Combine like terms: 6m2 + -6m2 = 0
-30 + -3m = -20 + 19m + 0
-30 + -3m = -20 + 19m

Solving
-30 + -3m = -20 + 19m

Solving for variable 'm'.

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

Add '-19m' to each side of the equation.
-30 + -3m + -19m = -20 + 19m + -19m

Combine like terms: -3m + -19m = -22m
-30 + -22m = -20 + 19m + -19m

Combine like terms: 19m + -19m = 0
-30 + -22m = -20 + 0
-30 + -22m = -20

Add '30' to each side of the equation.
-30 + 30 + -22m = -20 + 30

Combine like terms: -30 + 30 = 0
0 + -22m = -20 + 30
-22m = -20 + 30

Combine like terms: -20 + 30 = 10
-22m = 10

Divide each side by '-22'.
m = -0.4545454545

Simplifying
m = -0.4545454545

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