t(3t+14)=5

Solution for t(3t+14)=5 equation:

Simplifying
t(3t + 14) = 5

Reorder the terms:
t(14 + 3t) = 5
(14 * t + 3t * t) = 5
(14t + 3t2) = 5

Solving
14t + 3t2 = 5

Solving for variable 't'.

Reorder the terms:
-5 + 14t + 3t2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 14t + 3t2 = 0

Factor a trinomial.
(-5 + -1t)(1 + -3t) = 0

Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve:

Simplifying
-5 + -1t = 0

Solving
-5 + -1t = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1t = 0 + 5
-1t = 0 + 5

Combine like terms: 0 + 5 = 5
-1t = 5

Divide each side by '-1'.
t = -5

Simplifying
t = -5
Subproblem 2
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 = {-5, 0.3333333333}