(2n-7)(5n+20)=0

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Solution for (2n-7)(5n+20)=0 equation: 


Simplifying
(2n + -7)(5n + 20) = 0

Reorder the terms:
(-7 + 2n)(5n + 20) = 0

Reorder the terms:
(-7 + 2n)(20 + 5n) = 0

Multiply (-7 + 2n) * (20 + 5n)
(-7(20 + 5n) + 2n * (20 + 5n)) = 0
((20 * -7 + 5n * -7) + 2n * (20 + 5n)) = 0
((-140 + -35n) + 2n * (20 + 5n)) = 0
(-140 + -35n + (20 * 2n + 5n * 2n)) = 0
(-140 + -35n + (40n + 10n2)) = 0

Combine like terms: -35n + 40n = 5n
(-140 + 5n + 10n2) = 0

Solving
-140 + 5n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-28 + n + 2n2) = 0

Factor a trinomial.
5((-4 + -1n)(7 + -2n)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4

Subproblem 2
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
Solution
n = {-4, 3.5}

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