2t^2+2(2t)(-1)-1=4t^2+1

Solution for 2t^2+2(2t)(-1)-1=4t^2+1 equation:

Simplifying
2t2 + 2(2t)(-1) + -1 = 4t2 + 1

Remove parenthesis around (2t)
2t2 + 2 * 2t(-1) + -1 = 4t2 + 1

Reorder the terms for easier multiplication:
2t2 + 2 * 2 * -1t + -1 = 4t2 + 1

Multiply 2 * 2
2t2 + 4 * -1t + -1 = 4t2 + 1

Multiply 4 * -1
2t2 + -4t + -1 = 4t2 + 1

Reorder the terms:
-1 + -4t + 2t2 = 4t2 + 1

Reorder the terms:
-1 + -4t + 2t2 = 1 + 4t2

Solving
-1 + -4t + 2t2 = 1 + 4t2

Solving for variable 't'.

Reorder the terms:
-1 + -1 + -4t + 2t2 + -4t2 = 1 + 4t2 + -1 + -4t2

Combine like terms: -1 + -1 = -2
-2 + -4t + 2t2 + -4t2 = 1 + 4t2 + -1 + -4t2

Combine like terms: 2t2 + -4t2 = -2t2
-2 + -4t + -2t2 = 1 + 4t2 + -1 + -4t2

Reorder the terms:
-2 + -4t + -2t2 = 1 + -1 + 4t2 + -4t2

Combine like terms: 1 + -1 = 0
-2 + -4t + -2t2 = 0 + 4t2 + -4t2
-2 + -4t + -2t2 = 4t2 + -4t2

Combine like terms: 4t2 + -4t2 = 0
-2 + -4t + -2t2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 2t + t2) = 0

Factor a trinomial.
-2((1 + t)(1 + t)) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

Simplifying
t = -1
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

Simplifying
t = -1
Solution
t = {-1, -1}