(x+m)(x+m)=x(x-m)

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Solution for (x+m)(x+m)=x(x-m) equation: 


Simplifying
(x + m)(x + m) = x(x + -1m)

Reorder the terms:
(m + x)(x + m) = x(x + -1m)

Reorder the terms:
(m + x)(m + x) = x(x + -1m)

Multiply (m + x) * (m + x)
(m(m + x) + x(m + x)) = x(x + -1m)
((m * m + x * m) + x(m + x)) = x(x + -1m)

Reorder the terms:
((mx + m2) + x(m + x)) = x(x + -1m)
((mx + m2) + x(m + x)) = x(x + -1m)
(mx + m2 + (m * x + x * x)) = x(x + -1m)
(mx + m2 + (mx + x2)) = x(x + -1m)

Reorder the terms:
(mx + mx + m2 + x2) = x(x + -1m)

Combine like terms: mx + mx = 2mx
(2mx + m2 + x2) = x(x + -1m)

Reorder the terms:
2mx + m2 + x2 = x(-1m + x)
2mx + m2 + x2 = (-1m * x + x * x)
2mx + m2 + x2 = (-1mx + x2)

Add '-1x2' to each side of the equation.
2mx + m2 + x2 + -1x2 = -1mx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2mx + m2 + 0 = -1mx + x2 + -1x2
2mx + m2 = -1mx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2mx + m2 = -1mx + 0
2mx + m2 = -1mx

Solving
2mx + m2 = -1mx

Solving for variable 'm'.

Reorder the terms:
2mx + mx + m2 = -1mx + mx

Combine like terms: 2mx + mx = 3mx
3mx + m2 = -1mx + mx

Combine like terms: -1mx + mx = 0
3mx + m2 = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(3x + m) = 0


Subproblem 1
Set the factor 'm' equal to zero and attempt to solve:

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0

Subproblem 2
Set the factor '(3x + m)' equal to zero and attempt to solve:

Simplifying
3x + m = 0

Reorder the terms:
m + 3x = 0

Solving
m + 3x = 0

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

Add '-3x' to each side of the equation.
m + 3x + -3x = 0 + -3x

Combine like terms: 3x + -3x = 0
m + 0 = 0 + -3x
m = 0 + -3x
Remove the zero:
m = -3x

Simplifying
m = -3x
Solution
m = {0, -3x}

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