42t^2+t=30

Solution for 42t^2+t=30 equation:

Simplifying
42t2 + t = 30

Reorder the terms:
t + 42t2 = 30

Solving
t + 42t2 = 30

Solving for variable 't'.

Reorder the terms:
-30 + t + 42t2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + t + 42t2 = 0

Factor a trinomial.
(-6 + -7t)(5 + -6t) = 0

Subproblem 1
Set the factor '(-6 + -7t)' equal to zero and attempt to solve:

Simplifying
-6 + -7t = 0

Solving
-6 + -7t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -7t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7t = 0 + 6
-7t = 0 + 6

Combine like terms: 0 + 6 = 6
-7t = 6

Divide each side by '-7'.
t = -0.8571428571

Simplifying
t = -0.8571428571
Subproblem 2
Set the factor '(5 + -6t)' equal to zero and attempt to solve:

Simplifying
5 + -6t = 0

Solving
5 + -6t = 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 + -6t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6t = 0 + -5
-6t = 0 + -5

Combine like terms: 0 + -5 = -5
-6t = -5

Divide each side by '-6'.
t = 0.8333333333

Simplifying
t = 0.8333333333
Solution
t = {-0.8571428571, 0.8333333333}