(t-4)(t+1)=

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

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

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

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

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

Combine like terms: -4t + 1t = -3t
(-4 + -3t + t2) = 0

Solving
-4 + -3t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -1t)(4 + -1t) = 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 '(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 = {-1, 4}