(5n-5)*(5n+7)=0

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


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

Reorder the terms:
(-5 + 5n)(5n + 7) = 0

Reorder the terms:
(-5 + 5n)(7 + 5n) = 0

Multiply (-5 + 5n) * (7 + 5n)
(-5(7 + 5n) + 5n * (7 + 5n)) = 0
((7 * -5 + 5n * -5) + 5n * (7 + 5n)) = 0
((-35 + -25n) + 5n * (7 + 5n)) = 0
(-35 + -25n + (7 * 5n + 5n * 5n)) = 0
(-35 + -25n + (35n + 25n2)) = 0

Combine like terms: -25n + 35n = 10n
(-35 + 10n + 25n2) = 0

Solving
-35 + 10n + 25n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + 2n + 5n2) = 0

Factor a trinomial.
5((-7 + -5n)(1 + -1n)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -5n)' equal to zero and attempt to solve:

Simplifying
-7 + -5n = 0

Solving
-7 + -5n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -5n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5n = 0 + 7
-5n = 0 + 7

Combine like terms: 0 + 7 = 7
-5n = 7

Divide each side by '-5'.
n = -1.4

Simplifying
n = -1.4

Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {-1.4, 1}

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