(2n-8)(7n+3)=

Solution for (2n-8)(7n+3)= equation:

Simplifying
(2n + -8)(7n + 3) = 0

Reorder the terms:
(-8 + 2n)(7n + 3) = 0

Reorder the terms:
(-8 + 2n)(3 + 7n) = 0

Multiply (-8 + 2n) * (3 + 7n)
(-8(3 + 7n) + 2n * (3 + 7n)) = 0
((3 * -8 + 7n * -8) + 2n * (3 + 7n)) = 0
((-24 + -56n) + 2n * (3 + 7n)) = 0
(-24 + -56n + (3 * 2n + 7n * 2n)) = 0
(-24 + -56n + (6n + 14n2)) = 0

Combine like terms: -56n + 6n = -50n
(-24 + -50n + 14n2) = 0

Solving
-24 + -50n + 14n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -25n + 7n2) = 0

Factor a trinomial.
2((-3 + -7n)(4 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -7n)' equal to zero and attempt to solve:

Simplifying
-3 + -7n = 0

Solving
-3 + -7n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -7n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7n = 0 + 3
-7n = 0 + 3

Combine like terms: 0 + 3 = 3
-7n = 3

Divide each side by '-7'.
n = -0.4285714286

Simplifying
n = -0.4285714286
Subproblem 2
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
Solution
n = {-0.4285714286, 4}