4(c+2)(c+2)-1=0

Solution for 4(c+2)(c+2)-1=0 equation:

Simplifying
4(c + 2)(c + 2) + -1 = 0

Reorder the terms:
4(2 + c)(c + 2) + -1 = 0

Reorder the terms:
4(2 + c)(2 + c) + -1 = 0

Multiply (2 + c) * (2 + c)
4(2(2 + c) + c(2 + c)) + -1 = 0
4((2 * 2 + c * 2) + c(2 + c)) + -1 = 0
4((4 + 2c) + c(2 + c)) + -1 = 0
4(4 + 2c + (2 * c + c * c)) + -1 = 0
4(4 + 2c + (2c + c2)) + -1 = 0

Combine like terms: 2c + 2c = 4c
4(4 + 4c + c2) + -1 = 0
(4 * 4 + 4c * 4 + c2 * 4) + -1 = 0
(16 + 16c + 4c2) + -1 = 0

Reorder the terms:
16 + -1 + 16c + 4c2 = 0

Combine like terms: 16 + -1 = 15
15 + 16c + 4c2 = 0

Solving
15 + 16c + 4c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(5 + 2c)(3 + 2c) = 0

Subproblem 1
Set the factor '(5 + 2c)' equal to zero and attempt to solve:

Simplifying
5 + 2c = 0

Solving
5 + 2c = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2c = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2c = 0 + -5
2c = 0 + -5

Combine like terms: 0 + -5 = -5
2c = -5

Divide each side by '2'.
c = -2.5

Simplifying
c = -2.5
Subproblem 2
Set the factor '(3 + 2c)' equal to zero and attempt to solve:

Simplifying
3 + 2c = 0

Solving
3 + 2c = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2c = 0 + -3
2c = 0 + -3

Combine like terms: 0 + -3 = -3
2c = -3

Divide each side by '2'.
c = -1.5

Simplifying
c = -1.5
Solution
c = {-2.5, -1.5}