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

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

Simplifying
(2t + 1)(t + -4) = 0

Reorder the terms:
(1 + 2t)(t + -4) = 0

Reorder the terms:
(1 + 2t)(-4 + t) = 0

Multiply (1 + 2t) * (-4 + t)
(1(-4 + t) + 2t * (-4 + t)) = 0
((-4 * 1 + t * 1) + 2t * (-4 + t)) = 0
((-4 + 1t) + 2t * (-4 + t)) = 0
(-4 + 1t + (-4 * 2t + t * 2t)) = 0
(-4 + 1t + (-8t + 2t2)) = 0

Combine like terms: 1t + -8t = -7t
(-4 + -7t + 2t2) = 0

Solving
-4 + -7t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -2t)(4 + -1t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

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

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

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-0.5, 4}