(t^4)+(5t^3)-(14t^2)=0

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Solution for (t^4)+(5t^3)-(14t^2)=0 equation: 


Simplifying
(t4) + (5t3) + -1(14t2) = 0
t4 + (5t3) + -1(14t2) = 0

Remove parenthesis around (14t2)
t4 + (5t3) + -1 * 14t2 = 0

Multiply -1 * 14
t4 + (5t3) + -14t2 = 0

Reorder the terms:
-14t2 + (5t3) + t4 = 0

Solving
-14t2 + (5t3) + t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't2'.
t2(-14 + (5t) + t2) = 0

Factor a trinomial.
t2((-7 + -1t)(2 + -1t)) = 0


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

Simplifying
t2 = 0

Solving
t2 = 0

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

Simplifying
t2 = 0

Take the square root of each side:
t = {0}

Subproblem 2
Set the factor '(-7 + -1t)' equal to zero and attempt to solve:

Simplifying
-7 + -1t = 0

Solving
-7 + -1t = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1t = 0 + 7
-1t = 0 + 7

Combine like terms: 0 + 7 = 7
-1t = 7

Divide each side by '-1'.
t = -7

Simplifying
t = -7

Subproblem 3
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {0, -7, 2}

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