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

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


Simplifying
(t + -1)(t + 1)(t2 + 1) = 0

Reorder the terms:
(-1 + t)(t + 1)(t2 + 1) = 0

Reorder the terms:
(-1 + t)(1 + t)(t2 + 1) = 0

Reorder the terms:
(-1 + t)(1 + t)(1 + t2) = 0

Multiply (-1 + t) * (1 + t)
(-1(1 + t) + t(1 + t))(1 + t2) = 0
((1 * -1 + t * -1) + t(1 + t))(1 + t2) = 0
((-1 + -1t) + t(1 + t))(1 + t2) = 0
(-1 + -1t + (1 * t + t * t))(1 + t2) = 0
(-1 + -1t + (1t + t2))(1 + t2) = 0

Combine like terms: -1t + 1t = 0
(-1 + 0 + t2)(1 + t2) = 0
(-1 + t2)(1 + t2) = 0

Multiply (-1 + t2) * (1 + t2)
(-1(1 + t2) + t2(1 + t2)) = 0
((1 * -1 + t2 * -1) + t2(1 + t2)) = 0
((-1 + -1t2) + t2(1 + t2)) = 0
(-1 + -1t2 + (1 * t2 + t2 * t2)) = 0
(-1 + -1t2 + (1t2 + t4)) = 0

Combine like terms: -1t2 + 1t2 = 0
(-1 + 0 + t4) = 0
(-1 + t4) = 0

Solving
-1 + t4 = 0

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + t4 = 0 + 1
t4 = 0 + 1

Combine like terms: 0 + 1 = 1
t4 = 1

Simplifying
t4 = 1

Reorder the terms:
-1 + t4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + t4 = 0

Factor a difference between two squares.
(1 + t2)(-1 + t2) = 0

Factor a difference between two squares.
(1 + t2)((1 + t)(-1 + t)) = 0


Subproblem 1
Set the factor '(1 + t2)' equal to zero and attempt to solve:

Simplifying
1 + t2 = 0

Solving
1 + t2 = 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 + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t2 = 0 + -1
t2 = 0 + -1

Combine like terms: 0 + -1 = -1
t2 = -1

Simplifying
t2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Subproblem 3
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}

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