(4n-3)(2n+1)=7

Solution for (4n-3)(2n+1)=7 equation:

Simplifying
(4n + -3)(2n + 1) = 7

Reorder the terms:
(-3 + 4n)(2n + 1) = 7

Reorder the terms:
(-3 + 4n)(1 + 2n) = 7

Multiply (-3 + 4n) * (1 + 2n)
(-3(1 + 2n) + 4n * (1 + 2n)) = 7
((1 * -3 + 2n * -3) + 4n * (1 + 2n)) = 7
((-3 + -6n) + 4n * (1 + 2n)) = 7
(-3 + -6n + (1 * 4n + 2n * 4n)) = 7
(-3 + -6n + (4n + 8n2)) = 7

Combine like terms: -6n + 4n = -2n
(-3 + -2n + 8n2) = 7

Solving
-3 + -2n + 8n2 = 7

Solving for variable 'n'.

Reorder the terms:
-3 + -7 + -2n + 8n2 = 7 + -7

Combine like terms: -3 + -7 = -10
-10 + -2n + 8n2 = 7 + -7

Combine like terms: 7 + -7 = 0
-10 + -2n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -1n + 4n2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -4n)' equal to zero and attempt to solve:

Simplifying
5 + -4n = 0

Solving
5 + -4n = 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 + -4n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4n = 0 + -5
-4n = 0 + -5

Combine like terms: 0 + -5 = -5
-4n = -5

Divide each side by '-4'.
n = 1.25

Simplifying
n = 1.25
Solution
n = {-1, 1.25}