(mx+1)(x+m)=(mx+1)(2x+m)

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Solution for (mx+1)(x+m)=(mx+1)(2x+m) equation: 


Simplifying
(mx + 1)(x + m) = (mx + 1)(2x + m)

Reorder the terms:
(1 + mx)(x + m) = (mx + 1)(2x + m)

Reorder the terms:
(1 + mx)(m + x) = (mx + 1)(2x + m)

Multiply (1 + mx) * (m + x)
(1(m + x) + mx(m + x)) = (mx + 1)(2x + m)
((m * 1 + x * 1) + mx(m + x)) = (mx + 1)(2x + m)
((1m + 1x) + mx(m + x)) = (mx + 1)(2x + m)
(1m + 1x + (m * mx + x * mx)) = (mx + 1)(2x + m)

Reorder the terms:
(1m + 1x + (mx2 + m2x)) = (mx + 1)(2x + m)
(1m + 1x + (mx2 + m2x)) = (mx + 1)(2x + m)

Reorder the terms:
(1m + mx2 + m2x + 1x) = (mx + 1)(2x + m)
(1m + mx2 + m2x + 1x) = (mx + 1)(2x + m)

Reorder the terms:
1m + mx2 + m2x + 1x = (1 + mx)(2x + m)

Reorder the terms:
1m + mx2 + m2x + 1x = (1 + mx)(m + 2x)

Multiply (1 + mx) * (m + 2x)
1m + mx2 + m2x + 1x = (1(m + 2x) + mx(m + 2x))
1m + mx2 + m2x + 1x = ((m * 1 + 2x * 1) + mx(m + 2x))
1m + mx2 + m2x + 1x = ((1m + 2x) + mx(m + 2x))
1m + mx2 + m2x + 1x = (1m + 2x + (m * mx + 2x * mx))

Reorder the terms:
1m + mx2 + m2x + 1x = (1m + 2x + (2mx2 + m2x))
1m + mx2 + m2x + 1x = (1m + 2x + (2mx2 + m2x))

Reorder the terms:
1m + mx2 + m2x + 1x = (1m + 2mx2 + m2x + 2x)
1m + mx2 + m2x + 1x = (1m + 2mx2 + m2x + 2x)

Add '-1m' to each side of the equation.
1m + mx2 + m2x + -1m + 1x = 1m + 2mx2 + m2x + -1m + 2x

Reorder the terms:
1m + -1m + mx2 + m2x + 1x = 1m + 2mx2 + m2x + -1m + 2x

Combine like terms: 1m + -1m = 0
0 + mx2 + m2x + 1x = 1m + 2mx2 + m2x + -1m + 2x
mx2 + m2x + 1x = 1m + 2mx2 + m2x + -1m + 2x

Reorder the terms:
mx2 + m2x + 1x = 1m + -1m + 2mx2 + m2x + 2x

Combine like terms: 1m + -1m = 0
mx2 + m2x + 1x = 0 + 2mx2 + m2x + 2x
mx2 + m2x + 1x = 2mx2 + m2x + 2x

Add '-1m2x' to each side of the equation.
mx2 + m2x + -1m2x + 1x = 2mx2 + m2x + -1m2x + 2x

Combine like terms: m2x + -1m2x = 0
mx2 + 0 + 1x = 2mx2 + m2x + -1m2x + 2x
mx2 + 1x = 2mx2 + m2x + -1m2x + 2x

Combine like terms: m2x + -1m2x = 0
mx2 + 1x = 2mx2 + 0 + 2x
mx2 + 1x = 2mx2 + 2x

Solving
mx2 + 1x = 2mx2 + 2x

Solving for variable 'm'.

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

Add '-2mx2' to each side of the equation.
mx2 + -2mx2 + 1x = 2mx2 + -2mx2 + 2x

Combine like terms: mx2 + -2mx2 = -1mx2
-1mx2 + 1x = 2mx2 + -2mx2 + 2x

Combine like terms: 2mx2 + -2mx2 = 0
-1mx2 + 1x = 0 + 2x
-1mx2 + 1x = 2x

Add '-1x' to each side of the equation.
-1mx2 + 1x + -1x = 2x + -1x

Combine like terms: 1x + -1x = 0
-1mx2 + 0 = 2x + -1x
-1mx2 = 2x + -1x

Combine like terms: 2x + -1x = 1x
-1mx2 = 1x

Divide each side by '-1x2'.
m = -1x-1

Simplifying
m = -1x-1

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