5t^2+t=42

Solution for 5t^2+t=42 equation:

Simplifying
5t2 + t = 42

Reorder the terms:
t + 5t2 = 42

Solving
t + 5t2 = 42

Solving for variable 't'.

Reorder the terms:
-42 + t + 5t2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + t + 5t2 = 0

Factor a trinomial.
(-3 + -1t)(14 + -5t) = 0

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

Simplifying
-3 + -1t = 0

Solving
-3 + -1t = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1t = 0 + 3

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

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

Divide each side by '-1'.
t = -3

Simplifying
t = -3
Subproblem 2
Set the factor '(14 + -5t)' equal to zero and attempt to solve:

Simplifying
14 + -5t = 0

Solving
14 + -5t = 0

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

Add '-14' to each side of the equation.
14 + -14 + -5t = 0 + -14

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

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

Divide each side by '-5'.
t = 2.8

Simplifying
t = 2.8
Solution
t = {-3, 2.8}