4m+2mn+m^2=m+3m^2

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Solution for 4m+2mn+m^2=m+3m^2 equation:


Simplifying
4m + 2mn + m2 = m + 3m2

Solving
4m + 2mn + m2 = m + 3m2

Solving for variable 'm'.

Reorder the terms:
4m + -1m + 2mn + m2 + -3m2 = m + 3m2 + -1m + -3m2

Combine like terms: 4m + -1m = 3m
3m + 2mn + m2 + -3m2 = m + 3m2 + -1m + -3m2

Combine like terms: m2 + -3m2 = -2m2
3m + 2mn + -2m2 = m + 3m2 + -1m + -3m2

Reorder the terms:
3m + 2mn + -2m2 = m + -1m + 3m2 + -3m2

Combine like terms: m + -1m = 0
3m + 2mn + -2m2 = 0 + 3m2 + -3m2
3m + 2mn + -2m2 = 3m2 + -3m2

Combine like terms: 3m2 + -3m2 = 0
3m + 2mn + -2m2 = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(3 + 2n + -2m) = 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 '(3 + 2n + -2m)' equal to zero and attempt to solve: Simplifying 3 + 2n + -2m = 0 Reorder the terms: 3 + -2m + 2n = 0 Solving 3 + -2m + 2n = 0 Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -2m + -3 + 2n = 0 + -3 Reorder the terms: 3 + -3 + -2m + 2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2m + 2n = 0 + -3 -2m + 2n = 0 + -3 Combine like terms: 0 + -3 = -3 -2m + 2n = -3 Add '-2n' to each side of the equation. -2m + 2n + -2n = -3 + -2n Combine like terms: 2n + -2n = 0 -2m + 0 = -3 + -2n -2m = -3 + -2n Divide each side by '-2'. m = 1.5 + n Simplifying m = 1.5 + n

Solution

m = {0, 1.5 + n}

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