(4t^3+3t^2)-(t^3+t^2+t)=

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Solution for (4t^3+3t^2)-(t^3+t^2+t)= equation: 


Simplifying
(4t3 + 3t2) + -1(t3 + t2 + t) = 0

Reorder the terms:
(3t2 + 4t3) + -1(t3 + t2 + t) = 0

Remove parenthesis around (3t2 + 4t3)
3t2 + 4t3 + -1(t3 + t2 + t) = 0

Reorder the terms:
3t2 + 4t3 + -1(t + t2 + t3) = 0
3t2 + 4t3 + (t * -1 + t2 * -1 + t3 * -1) = 0
3t2 + 4t3 + (-1t + -1t2 + -1t3) = 0

Reorder the terms:
-1t + 3t2 + -1t2 + 4t3 + -1t3 = 0

Combine like terms: 3t2 + -1t2 = 2t2
-1t + 2t2 + 4t3 + -1t3 = 0

Combine like terms: 4t3 + -1t3 = 3t3
-1t + 2t2 + 3t3 = 0

Solving
-1t + 2t2 + 3t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-1 + 2t + 3t2) = 0

Factor a trinomial.
t((-1 + -1t)(1 + -3t)) = 0


Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0

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

Simplifying
-1 + -1t = 0

Solving
-1 + -1t = 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 + -1t = 0 + 1

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

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

Divide each side by '-1'.
t = -1

Simplifying
t = -1

Subproblem 3
Set the factor '(1 + -3t)' equal to zero and attempt to solve:

Simplifying
1 + -3t = 0

Solving
1 + -3t = 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 + -3t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3t = 0 + -1
-3t = 0 + -1

Combine like terms: 0 + -1 = -1
-3t = -1

Divide each side by '-3'.
t = 0.3333333333

Simplifying
t = 0.3333333333
Solution
t = {0, -1, 0.3333333333}

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