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

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


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

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

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

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

Combine like terms: 4m + -5m = -1m
(-20 + -1m + m2) = (m + -5)(m + 8)

Reorder the terms:
-20 + -1m + m2 = (-5 + m)(m + 8)

Reorder the terms:
-20 + -1m + m2 = (-5 + m)(8 + m)

Multiply (-5 + m) * (8 + m)
-20 + -1m + m2 = (-5(8 + m) + m(8 + m))
-20 + -1m + m2 = ((8 * -5 + m * -5) + m(8 + m))
-20 + -1m + m2 = ((-40 + -5m) + m(8 + m))
-20 + -1m + m2 = (-40 + -5m + (8 * m + m * m))
-20 + -1m + m2 = (-40 + -5m + (8m + m2))

Combine like terms: -5m + 8m = 3m
-20 + -1m + m2 = (-40 + 3m + m2)

Add '-1m2' to each side of the equation.
-20 + -1m + m2 + -1m2 = -40 + 3m + m2 + -1m2

Combine like terms: m2 + -1m2 = 0
-20 + -1m + 0 = -40 + 3m + m2 + -1m2
-20 + -1m = -40 + 3m + m2 + -1m2

Combine like terms: m2 + -1m2 = 0
-20 + -1m = -40 + 3m + 0
-20 + -1m = -40 + 3m

Solving
-20 + -1m = -40 + 3m

Solving for variable 'm'.

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

Add '-3m' to each side of the equation.
-20 + -1m + -3m = -40 + 3m + -3m

Combine like terms: -1m + -3m = -4m
-20 + -4m = -40 + 3m + -3m

Combine like terms: 3m + -3m = 0
-20 + -4m = -40 + 0
-20 + -4m = -40

Add '20' to each side of the equation.
-20 + 20 + -4m = -40 + 20

Combine like terms: -20 + 20 = 0
0 + -4m = -40 + 20
-4m = -40 + 20

Combine like terms: -40 + 20 = -20
-4m = -20

Divide each side by '-4'.
m = 5

Simplifying
m = 5

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