0=42+29t-5t^2

Solution for 0=42+29t-5t^2 equation:

Simplifying
0 = 42 + 29t + -5t2

Solving
0 = 42 + 29t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -42 = -42
-42 + -29t + 5t2 = 42 + 29t + -5t2 + -42 + -29t + 5t2

Reorder the terms:
-42 + -29t + 5t2 = 42 + -42 + 29t + -29t + -5t2 + 5t2

Combine like terms: 42 + -42 = 0
-42 + -29t + 5t2 = 0 + 29t + -29t + -5t2 + 5t2
-42 + -29t + 5t2 = 29t + -29t + -5t2 + 5t2

Combine like terms: 29t + -29t = 0
-42 + -29t + 5t2 = 0 + -5t2 + 5t2
-42 + -29t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-42 + -29t + 5t2 = 0

Factor a trinomial.
(-6 + -5t)(7 + -1t) = 0

Subproblem 1
Set the factor '(-6 + -5t)' equal to zero and attempt to solve:

Simplifying
-6 + -5t = 0

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

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

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

Divide each side by '-5'.
t = -1.2

Simplifying
t = -1.2
Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve:

Simplifying
7 + -1t = 0

Solving
7 + -1t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t = 0 + -7
-1t = 0 + -7

Combine like terms: 0 + -7 = -7
-1t = -7

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Solution
t = {-1.2, 7}