-15=(t+6)(t-2)

Solution for -15=(t+6)(t-2) equation:

Simplifying
-15 = (t + 6)(t + -2)

Reorder the terms:
-15 = (6 + t)(t + -2)

Reorder the terms:
-15 = (6 + t)(-2 + t)

Multiply (6 + t) * (-2 + t)
-15 = (6(-2 + t) + t(-2 + t))
-15 = ((-2 * 6 + t * 6) + t(-2 + t))
-15 = ((-12 + 6t) + t(-2 + t))
-15 = (-12 + 6t + (-2 * t + t * t))
-15 = (-12 + 6t + (-2t + t2))

Combine like terms: 6t + -2t = 4t
-15 = (-12 + 4t + t2)

Solving
-15 = -12 + 4t + t2

Solving for variable 't'.

Combine like terms: -15 + 12 = -3
-3 + -4t + -1t2 = -12 + 4t + t2 + 12 + -4t + -1t2

Reorder the terms:
-3 + -4t + -1t2 = -12 + 12 + 4t + -4t + t2 + -1t2

Combine like terms: -12 + 12 = 0
-3 + -4t + -1t2 = 0 + 4t + -4t + t2 + -1t2
-3 + -4t + -1t2 = 4t + -4t + t2 + -1t2

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 4t + t2) = 0

Factor a trinomial.
-1((3 + t)(1 + t)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
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 = {-3, -1}