t^2=7t-6

Solution for t^2=7t-6 equation:

Simplifying
t2 = 7t + -6

Reorder the terms:
t2 = -6 + 7t

Solving
t2 = -6 + 7t

Solving for variable 't'.

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

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

Combine like terms: -6 + 6 = 0
6 + -7t + t2 = 0 + 7t + -7t
6 + -7t + t2 = 7t + -7t

Combine like terms: 7t + -7t = 0
6 + -7t + t2 = 0

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

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

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

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

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

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

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

Simplifying
t = 1
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 = {1, 6}