8t^2+5t-42=0

Solution for 8t^2+5t-42=0 equation:

Simplifying
8t2 + 5t + -42 = 0

Reorder the terms:
-42 + 5t + 8t2 = 0

Solving
-42 + 5t + 8t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-21 + -8t)(2 + -1t) = 0

Subproblem 1
Set the factor '(-21 + -8t)' equal to zero and attempt to solve:

Simplifying
-21 + -8t = 0

Solving
-21 + -8t = 0

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

Add '21' to each side of the equation.
-21 + 21 + -8t = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -8t = 0 + 21
-8t = 0 + 21

Combine like terms: 0 + 21 = 21
-8t = 21

Divide each side by '-8'.
t = -2.625

Simplifying
t = -2.625
Subproblem 2
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 = {-2.625, 2}