(n-1)(7n+5)=0

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Solution for (n-1)(7n+5)=0 equation:


Simplifying
(n + -1)(7n + 5) = 0

Reorder the terms:
(-1 + n)(7n + 5) = 0

Reorder the terms:
(-1 + n)(5 + 7n) = 0

Multiply (-1 + n) * (5 + 7n)
(-1(5 + 7n) + n(5 + 7n)) = 0
((5 * -1 + 7n * -1) + n(5 + 7n)) = 0
((-5 + -7n) + n(5 + 7n)) = 0
(-5 + -7n + (5 * n + 7n * n)) = 0
(-5 + -7n + (5n + 7n2)) = 0

Combine like terms: -7n + 5n = -2n
(-5 + -2n + 7n2) = 0

Solving
-5 + -2n + 7n2 = 0

Solving for variable 'n'.

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

Subproblem 1

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

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 = {-0.7142857143, 1}

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