4t^2+t=33

Solution for 4t^2+t=33 equation:

Simplifying
4t2 + t = 33

Reorder the terms:
t + 4t2 = 33

Solving
t + 4t2 = 33

Solving for variable 't'.

Reorder the terms:
-33 + t + 4t2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + t + 4t2 = 0

Factor a trinomial.
(-3 + -1t)(11 + -4t) = 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 '(11 + -4t)' equal to zero and attempt to solve:

Simplifying
11 + -4t = 0

Solving
11 + -4t = 0

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

Add '-11' to each side of the equation.
11 + -11 + -4t = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4t = 0 + -11
-4t = 0 + -11

Combine like terms: 0 + -11 = -11
-4t = -11

Divide each side by '-4'.
t = 2.75

Simplifying
t = 2.75
Solution
t = {-3, 2.75}