77-4t=t^2

Solution for 77-4t=t^2 equation:

Simplifying
77 + -4t = t2

Solving
77 + -4t = t2

Solving for variable 't'.

Combine like terms: t2 + -1t2 = 0
77 + -4t + -1t2 = 0

Factor a trinomial.
(7 + -1t)(11 + t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(11 + t)' equal to zero and attempt to solve:

Simplifying
11 + t = 0

Solving
11 + t = 0

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

Add '-11' to each side of the equation.
11 + -11 + t = 0 + -11

Combine like terms: 11 + -11 = 0
0 + t = 0 + -11
t = 0 + -11

Combine like terms: 0 + -11 = -11
t = -11

Simplifying
t = -11
Solution
t = {7, -11}