7t^2-t-26=0

Solution for 7t^2-t-26=0 equation:

Simplifying
7t2 + -1t + -26 = 0

Reorder the terms:
-26 + -1t + 7t2 = 0

Solving
-26 + -1t + 7t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-13 + -7t)(2 + -1t) = 0

Subproblem 1
Set the factor '(-13 + -7t)' equal to zero and attempt to solve:

Simplifying
-13 + -7t = 0

Solving
-13 + -7t = 0

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

Add '13' to each side of the equation.
-13 + 13 + -7t = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -7t = 0 + 13
-7t = 0 + 13

Combine like terms: 0 + 13 = 13
-7t = 13

Divide each side by '-7'.
t = -1.857142857

Simplifying
t = -1.857142857
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-1.857142857, 2}