7x^2+(m+n-5x)x(m-n+7)=0

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Solution for 7x^2+(m+n-5x)x(m-n+7)=0 equation:


Simplifying
7x2 + (m + n + -5x) * x(m + -1n + 7) = 0

Reorder the terms:
7x2 + (m + n + -5x) * x(7 + m + -1n) = 0

Reorder the terms for easier multiplication:
7x2 + x(m + n + -5x)(7 + m + -1n) = 0

Multiply (m + n + -5x) * (7 + m + -1n)
7x2 + x(m(7 + m + -1n) + n(7 + m + -1n) + -5x * (7 + m + -1n)) = 0
7x2 + x((7 * m + m * m + -1n * m) + n(7 + m + -1n) + -5x * (7 + m + -1n)) = 0

Reorder the terms:
7x2 + x((7m + -1mn + m2) + n(7 + m + -1n) + -5x * (7 + m + -1n)) = 0
7x2 + x((7m + -1mn + m2) + n(7 + m + -1n) + -5x * (7 + m + -1n)) = 0
7x2 + x(7m + -1mn + m2 + (7 * n + m * n + -1n * n) + -5x * (7 + m + -1n)) = 0

Reorder the terms:
7x2 + x(7m + -1mn + m2 + (mn + 7n + -1n2) + -5x * (7 + m + -1n)) = 0
7x2 + x(7m + -1mn + m2 + (mn + 7n + -1n2) + -5x * (7 + m + -1n)) = 0
7x2 + x(7m + -1mn + m2 + mn + 7n + -1n2 + (7 * -5x + m * -5x + -1n * -5x)) = 0

Reorder the terms:
7x2 + x(7m + -1mn + m2 + mn + 7n + -1n2 + (-5mx + 5nx + -35x)) = 0
7x2 + x(7m + -1mn + m2 + mn + 7n + -1n2 + (-5mx + 5nx + -35x)) = 0

Reorder the terms:
7x2 + x(7m + -1mn + mn + -5mx + m2 + 7n + 5nx + -1n2 + -35x) = 0

Combine like terms: -1mn + mn = 0
7x2 + x(7m + 0 + -5mx + m2 + 7n + 5nx + -1n2 + -35x) = 0
7x2 + x(7m + -5mx + m2 + 7n + 5nx + -1n2 + -35x) = 0
7x2 + (7m * x + -5mx * x + m2 * x + 7n * x + 5nx * x + -1n2 * x + -35x * x) = 0
7x2 + (7mx + -5mx2 + m2x + 7nx + 5nx2 + -1n2x + -35x2) = 0

Reorder the terms:
7mx + -5mx2 + m2x + 7nx + 5nx2 + -1n2x + 7x2 + -35x2 = 0

Combine like terms: 7x2 + -35x2 = -28x2
7mx + -5mx2 + m2x + 7nx + 5nx2 + -1n2x + -28x2 = 0

Solving
7mx + -5mx2 + m2x + 7nx + 5nx2 + -1n2x + -28x2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7m + -5mx + m2 + 7n + 5nx + -1n2 + -28x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(7m + -5mx + m2 + 7n + 5nx + -1n2 + -28x)' equal to zero and attempt to solve: Simplifying 7m + -5mx + m2 + 7n + 5nx + -1n2 + -28x = 0 Solving 7m + -5mx + m2 + 7n + 5nx + -1n2 + -28x = 0 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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