(7m+5n)(7m+5n)=0

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Solution for (7m+5n)(7m+5n)=0 equation:


Simplifying
(7m + 5n)(7m + 5n) = 0

Multiply (7m + 5n) * (7m + 5n)
(7m * (7m + 5n) + 5n * (7m + 5n)) = 0
((7m * 7m + 5n * 7m) + 5n * (7m + 5n)) = 0

Reorder the terms:
((35mn + 49m2) + 5n * (7m + 5n)) = 0
((35mn + 49m2) + 5n * (7m + 5n)) = 0
(35mn + 49m2 + (7m * 5n + 5n * 5n)) = 0
(35mn + 49m2 + (35mn + 25n2)) = 0

Reorder the terms:
(35mn + 35mn + 49m2 + 25n2) = 0

Combine like terms: 35mn + 35mn = 70mn
(70mn + 49m2 + 25n2) = 0

Solving
70mn + 49m2 + 25n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(7m + 5n)(7m + 5n) = 0

Subproblem 1

Set the factor '(7m + 5n)' equal to zero and attempt to solve: Simplifying 7m + 5n = 0 Solving 7m + 5n = 0 Move all terms containing m to the left, all other terms to the right. Add '-5n' to each side of the equation. 7m + 5n + -5n = 0 + -5n Combine like terms: 5n + -5n = 0 7m + 0 = 0 + -5n 7m = 0 + -5n Remove the zero: 7m = -5n Divide each side by '7'. m = -0.7142857143n Simplifying m = -0.7142857143n

Subproblem 2

Set the factor '(7m + 5n)' equal to zero and attempt to solve: Simplifying 7m + 5n = 0 Solving 7m + 5n = 0 Move all terms containing m to the left, all other terms to the right. Add '-5n' to each side of the equation. 7m + 5n + -5n = 0 + -5n Combine like terms: 5n + -5n = 0 7m + 0 = 0 + -5n 7m = 0 + -5n Remove the zero: 7m = -5n Divide each side by '7'. m = -0.7142857143n Simplifying m = -0.7142857143n

Solution

m = {-0.7142857143n, -0.7142857143n}

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