n(4n-5)+(1-2n)(1+2n)=-9

Solution for n(4n-5)+(1-2n)(1+2n)=-9 equation:

Simplifying
n(4n + -5) + (1 + -2n)(1 + 2n) = -9

Reorder the terms:
n(-5 + 4n) + (1 + -2n)(1 + 2n) = -9
(-5 * n + 4n * n) + (1 + -2n)(1 + 2n) = -9
(-5n + 4n2) + (1 + -2n)(1 + 2n) = -9

Multiply (1 + -2n) * (1 + 2n)
-5n + 4n2 + (1(1 + 2n) + -2n * (1 + 2n)) = -9
-5n + 4n2 + ((1 * 1 + 2n * 1) + -2n * (1 + 2n)) = -9
-5n + 4n2 + ((1 + 2n) + -2n * (1 + 2n)) = -9
-5n + 4n2 + (1 + 2n + (1 * -2n + 2n * -2n)) = -9
-5n + 4n2 + (1 + 2n + (-2n + -4n2)) = -9

Combine like terms: 2n + -2n = 0
-5n + 4n2 + (1 + 0 + -4n2) = -9
-5n + 4n2 + (1 + -4n2) = -9

Reorder the terms:
1 + -5n + 4n2 + -4n2 = -9

Combine like terms: 4n2 + -4n2 = 0
1 + -5n + 0 = -9
1 + -5n = -9

Solving
1 + -5n = -9

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + -5n = -9 + -1

Combine like terms: 1 + -1 = 0
0 + -5n = -9 + -1
-5n = -9 + -1

Combine like terms: -9 + -1 = -10
-5n = -10

Divide each side by '-5'.
n = 2

Simplifying
n = 2