30=-7t+t^2

Solution for 30=-7t+t^2 equation:

Simplifying
30 = -7t + t2

Solving
30 = -7t + t2

Solving for variable 't'.

Reorder the terms:
30 + 7t + -1t2 = -7t + 7t + t2 + -1t2

Combine like terms: -7t + 7t = 0
30 + 7t + -1t2 = 0 + t2 + -1t2
30 + 7t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
30 + 7t + -1t2 = 0

Factor a trinomial.
(10 + -1t)(3 + t) = 0

Subproblem 1
Set the factor '(10 + -1t)' equal to zero and attempt to solve:

Simplifying
10 + -1t = 0

Solving
10 + -1t = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1t = 0 + -10
-1t = 0 + -10

Combine like terms: 0 + -10 = -10
-1t = -10

Divide each side by '-1'.
t = 10

Simplifying
t = 10
Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 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 + t = 0 + -3

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

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

Simplifying
t = -3
Solution
t = {10, -3}