7t^2+6t-45=0

Solution for 7t^2+6t-45=0 equation:

Simplifying
7t2 + 6t + -45 = 0

Reorder the terms:
-45 + 6t + 7t2 = 0

Solving
-45 + 6t + 7t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-3 + -1t)(15 + -7t) = 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 '(15 + -7t)' equal to zero and attempt to solve:

Simplifying
15 + -7t = 0

Solving
15 + -7t = 0

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

Add '-15' to each side of the equation.
15 + -15 + -7t = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -7t = 0 + -15
-7t = 0 + -15

Combine like terms: 0 + -15 = -15
-7t = -15

Divide each side by '-7'.
t = 2.142857143

Simplifying
t = 2.142857143
Solution
t = {-3, 2.142857143}