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

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

Simplifying
(5t + 1)(t + -5) = 0

Reorder the terms:
(1 + 5t)(t + -5) = 0

Reorder the terms:
(1 + 5t)(-5 + t) = 0

Multiply (1 + 5t) * (-5 + t)
(1(-5 + t) + 5t * (-5 + t)) = 0
((-5 * 1 + t * 1) + 5t * (-5 + t)) = 0
((-5 + 1t) + 5t * (-5 + t)) = 0
(-5 + 1t + (-5 * 5t + t * 5t)) = 0
(-5 + 1t + (-25t + 5t2)) = 0

Combine like terms: 1t + -25t = -24t
(-5 + -24t + 5t2) = 0

Solving
-5 + -24t + 5t2 = 0

Solving for variable 't'.

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

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

Simplifying
-1 + -5t = 0

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

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

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

Divide each side by '-5'.
t = -0.2

Simplifying
t = -0.2
Subproblem 2
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
Solution
t = {-0.2, 5}