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

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

Simplifying
(t + 5)(2t + -1) = 0

Reorder the terms:
(5 + t)(2t + -1) = 0

Reorder the terms:
(5 + t)(-1 + 2t) = 0

Multiply (5 + t) * (-1 + 2t)
(5(-1 + 2t) + t(-1 + 2t)) = 0
((-1 * 5 + 2t * 5) + t(-1 + 2t)) = 0
((-5 + 10t) + t(-1 + 2t)) = 0
(-5 + 10t + (-1 * t + 2t * t)) = 0
(-5 + 10t + (-1t + 2t2)) = 0

Combine like terms: 10t + -1t = 9t
(-5 + 9t + 2t2) = 0

Solving
-5 + 9t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -1t)(1 + -2t) = 0

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

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

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

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

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {-5, 0.5}