(n-7)(2n+7)=0

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Solution for (n-7)(2n+7)=0 equation: 


Simplifying
(n + -7)(2n + 7) = 0

Reorder the terms:
(-7 + n)(2n + 7) = 0

Reorder the terms:
(-7 + n)(7 + 2n) = 0

Multiply (-7 + n) * (7 + 2n)
(-7(7 + 2n) + n(7 + 2n)) = 0
((7 * -7 + 2n * -7) + n(7 + 2n)) = 0
((-49 + -14n) + n(7 + 2n)) = 0
(-49 + -14n + (7 * n + 2n * n)) = 0
(-49 + -14n + (7n + 2n2)) = 0

Combine like terms: -14n + 7n = -7n
(-49 + -7n + 2n2) = 0

Solving
-49 + -7n + 2n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-7 + -2n)(7 + -1n) = 0


Subproblem 1
Set the factor '(-7 + -2n)' equal to zero and attempt to solve:

Simplifying
-7 + -2n = 0

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

Combine like terms: -7 + 7 = 0
0 + -2n = 0 + 7
-2n = 0 + 7

Combine like terms: 0 + 7 = 7
-2n = 7

Divide each side by '-2'.
n = -3.5

Simplifying
n = -3.5

Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 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 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-3.5, 7}

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