t^2-7t+21=4t-9

Solution for t^2-7t+21=4t-9 equation:

Simplifying
t2 + -7t + 21 = 4t + -9

Reorder the terms:
21 + -7t + t2 = 4t + -9

Reorder the terms:
21 + -7t + t2 = -9 + 4t

Solving
21 + -7t + t2 = -9 + 4t

Solving for variable 't'.

Reorder the terms:
21 + 9 + -7t + -4t + t2 = -9 + 4t + 9 + -4t

Combine like terms: 21 + 9 = 30
30 + -7t + -4t + t2 = -9 + 4t + 9 + -4t

Combine like terms: -7t + -4t = -11t
30 + -11t + t2 = -9 + 4t + 9 + -4t

Reorder the terms:
30 + -11t + t2 = -9 + 9 + 4t + -4t

Combine like terms: -9 + 9 = 0
30 + -11t + t2 = 0 + 4t + -4t
30 + -11t + t2 = 4t + -4t

Combine like terms: 4t + -4t = 0
30 + -11t + t2 = 0

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

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

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 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 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {5, 6}