(m+n)(a-n)+(m+n)(a-n)=

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Solution for (m+n)(a-n)+(m+n)(a-n)= equation:


Simplifying
(m + n)(a + -1n) + (m + n)(a + -1n) = 0

Multiply (m + n) * (a + -1n)
(m(a + -1n) + n(a + -1n)) + (m + n)(a + -1n) = 0
((a * m + -1n * m) + n(a + -1n)) + (m + n)(a + -1n) = 0
((am + -1mn) + n(a + -1n)) + (m + n)(a + -1n) = 0
(am + -1mn + (a * n + -1n * n)) + (m + n)(a + -1n) = 0
(am + -1mn + (an + -1n2)) + (m + n)(a + -1n) = 0

Reorder the terms:
(am + an + -1mn + -1n2) + (m + n)(a + -1n) = 0
(am + an + -1mn + -1n2) + (m + n)(a + -1n) = 0

Multiply (m + n) * (a + -1n)
am + an + -1mn + -1n2 + (m(a + -1n) + n(a + -1n)) = 0
am + an + -1mn + -1n2 + ((a * m + -1n * m) + n(a + -1n)) = 0
am + an + -1mn + -1n2 + ((am + -1mn) + n(a + -1n)) = 0
am + an + -1mn + -1n2 + (am + -1mn + (a * n + -1n * n)) = 0
am + an + -1mn + -1n2 + (am + -1mn + (an + -1n2)) = 0

Reorder the terms:
am + an + -1mn + -1n2 + (am + an + -1mn + -1n2) = 0
am + an + -1mn + -1n2 + (am + an + -1mn + -1n2) = 0

Reorder the terms:
am + am + an + an + -1mn + -1mn + -1n2 + -1n2 = 0

Combine like terms: am + am = 2am
2am + an + an + -1mn + -1mn + -1n2 + -1n2 = 0

Combine like terms: an + an = 2an
2am + 2an + -1mn + -1mn + -1n2 + -1n2 = 0

Combine like terms: -1mn + -1mn = -2mn
2am + 2an + -2mn + -1n2 + -1n2 = 0

Combine like terms: -1n2 + -1n2 = -2n2
2am + 2an + -2mn + -2n2 = 0

Solving
2am + 2an + -2mn + -2n2 = 0

Solving for variable 'a'.

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

Add '2mn' to each side of the equation.
2am + 2an + -2mn + 2mn + -2n2 = 0 + 2mn

Combine like terms: -2mn + 2mn = 0
2am + 2an + 0 + -2n2 = 0 + 2mn
2am + 2an + -2n2 = 0 + 2mn
Remove the zero:
2am + 2an + -2n2 = 2mn

Add '2n2' to each side of the equation.
2am + 2an + -2n2 + 2n2 = 2mn + 2n2

Combine like terms: -2n2 + 2n2 = 0
2am + 2an + 0 = 2mn + 2n2
2am + 2an = 2mn + 2n2

Reorder the terms:
2am + 2an + -2mn + -2n2 = 2mn + -2mn + 2n2 + -2n2

Combine like terms: 2mn + -2mn = 0
2am + 2an + -2mn + -2n2 = 0 + 2n2 + -2n2
2am + 2an + -2mn + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
2am + 2an + -2mn + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(am + an + -1mn + -1n2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(am + an + -1mn + -1n2)' equal to zero and attempt to solve: Simplifying am + an + -1mn + -1n2 = 0 Solving am + an + -1mn + -1n2 = 0 Move all terms containing a to the left, all other terms to the right. Add 'mn' to each side of the equation. am + an + -1mn + mn + -1n2 = 0 + mn Combine like terms: -1mn + mn = 0 am + an + 0 + -1n2 = 0 + mn am + an + -1n2 = 0 + mn Remove the zero: am + an + -1n2 = mn Add 'n2' to each side of the equation. am + an + -1n2 + n2 = mn + n2 Combine like terms: -1n2 + n2 = 0 am + an + 0 = mn + n2 am + an = mn + n2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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