a^2-c^2-1-c^2=0

Solution for a^2-c^2-1-c^2=0 equation:

Simplifying
a2 + -1c2 + -1 + -1c2 = 0

Reorder the terms:
-1 + a2 + -1c2 + -1c2 = 0

Combine like terms: -1c2 + -1c2 = -2c2
-1 + a2 + -2c2 = 0

Solving
-1 + a2 + -2c2 = 0

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + a2 + 1 + -2c2 = 0 + 1

Reorder the terms:
-1 + 1 + a2 + -2c2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + a2 + -2c2 = 0 + 1
a2 + -2c2 = 0 + 1

Combine like terms: 0 + 1 = 1
a2 + -2c2 = 1

Add '2c2' to each side of the equation.
a2 + -2c2 + 2c2 = 1 + 2c2

Combine like terms: -2c2 + 2c2 = 0
a2 + 0 = 1 + 2c2
a2 = 1 + 2c2

Simplifying
a2 = 1 + 2c2

Reorder the terms:
-1 + a2 + -2c2 = 1 + 2c2 + -1 + -2c2

Reorder the terms:
-1 + a2 + -2c2 = 1 + -1 + 2c2 + -2c2

Combine like terms: 1 + -1 = 0
-1 + a2 + -2c2 = 0 + 2c2 + -2c2
-1 + a2 + -2c2 = 2c2 + -2c2

Combine like terms: 2c2 + -2c2 = 0
-1 + a2 + -2c2 = 0

Factor a trinomial.
(a + -2c)(a + c) = 0

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

Simplifying
a + -2c = 0

Solving
a + -2c = 0

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

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

Combine like terms: -2c + 2c = 0
a + 0 = 0 + 2c
a = 0 + 2c
Remove the zero:
a = 2c

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

Simplifying
a + c = 0

Solving
a + c = 0

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

Add '-1c' to each side of the equation.
a + c + -1c = 0 + -1c

Combine like terms: c + -1c = 0
a + 0 = 0 + -1c
a = 0 + -1c
Remove the zero:
a = -1c

Simplifying
a = -1c
Solution
a = {2c, -1c}