(t+4)(t-1)=-6

Solution for (t+4)(t-1)=-6 equation:

Simplifying
(t + 4)(t + -1) = -6

Reorder the terms:
(4 + t)(t + -1) = -6

Reorder the terms:
(4 + t)(-1 + t) = -6

Multiply (4 + t) * (-1 + t)
(4(-1 + t) + t(-1 + t)) = -6
((-1 * 4 + t * 4) + t(-1 + t)) = -6
((-4 + 4t) + t(-1 + t)) = -6
(-4 + 4t + (-1 * t + t * t)) = -6
(-4 + 4t + (-1t + t2)) = -6

Combine like terms: 4t + -1t = 3t
(-4 + 3t + t2) = -6

Solving
-4 + 3t + t2 = -6

Solving for variable 't'.

Reorder the terms:
-4 + 6 + 3t + t2 = -6 + 6

Combine like terms: -4 + 6 = 2
2 + 3t + t2 = -6 + 6

Combine like terms: -6 + 6 = 0
2 + 3t + t2 = 0

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

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

Simplifying
2 + t = 0

Solving
2 + t = 0

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

Add '-2' to each side of the equation.
2 + -2 + t = 0 + -2

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

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

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

Simplifying
1 + t = 0

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

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

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

Simplifying
t = -1
Solution
t = {-2, -1}