(t-1)(5t+4)=2

Solution for (t-1)(5t+4)=2 equation:

Simplifying
(t + -1)(5t + 4) = 2

Reorder the terms:
(-1 + t)(5t + 4) = 2

Reorder the terms:
(-1 + t)(4 + 5t) = 2

Multiply (-1 + t) * (4 + 5t)
(-1(4 + 5t) + t(4 + 5t)) = 2
((4 * -1 + 5t * -1) + t(4 + 5t)) = 2
((-4 + -5t) + t(4 + 5t)) = 2
(-4 + -5t + (4 * t + 5t * t)) = 2
(-4 + -5t + (4t + 5t2)) = 2

Combine like terms: -5t + 4t = -1t
(-4 + -1t + 5t2) = 2

Solving
-4 + -1t + 5t2 = 2

Solving for variable 't'.

Reorder the terms:
-4 + -2 + -1t + 5t2 = 2 + -2

Combine like terms: -4 + -2 = -6
-6 + -1t + 5t2 = 2 + -2

Combine like terms: 2 + -2 = 0
-6 + -1t + 5t2 = 0

Factor a trinomial.
(-1 + -1t)(6 + -5t) = 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 + -5t)' equal to zero and attempt to solve:

Simplifying
6 + -5t = 0

Solving
6 + -5t = 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 + -5t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5t = 0 + -6
-5t = 0 + -6

Combine like terms: 0 + -6 = -6
-5t = -6

Divide each side by '-5'.
t = 1.2

Simplifying
t = 1.2
Solution
t = {-1, 1.2}