-4=(t+2)(t+7)

Solution for -4=(t+2)(t+7) equation:

Simplifying
-4 = (t + 2)(t + 7)

Reorder the terms:
-4 = (2 + t)(t + 7)

Reorder the terms:
-4 = (2 + t)(7 + t)

Multiply (2 + t) * (7 + t)
-4 = (2(7 + t) + t(7 + t))
-4 = ((7 * 2 + t * 2) + t(7 + t))
-4 = ((14 + 2t) + t(7 + t))
-4 = (14 + 2t + (7 * t + t * t))
-4 = (14 + 2t + (7t + t2))

Combine like terms: 2t + 7t = 9t
-4 = (14 + 9t + t2)

Solving
-4 = 14 + 9t + t2

Solving for variable 't'.

Combine like terms: -4 + -14 = -18
-18 + -9t + -1t2 = 14 + 9t + t2 + -14 + -9t + -1t2

Reorder the terms:
-18 + -9t + -1t2 = 14 + -14 + 9t + -9t + t2 + -1t2

Combine like terms: 14 + -14 = 0
-18 + -9t + -1t2 = 0 + 9t + -9t + t2 + -1t2
-18 + -9t + -1t2 = 9t + -9t + t2 + -1t2

Combine like terms: 9t + -9t = 0
-18 + -9t + -1t2 = 0 + t2 + -1t2
-18 + -9t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-18 + -9t + -1t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 9t + t2) = 0

Factor a trinomial.
-1((6 + t)(3 + t)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 0

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

Add '-6' to each side of the equation.
6 + -6 + t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + t = 0 + -6
t = 0 + -6

Combine like terms: 0 + -6 = -6
t = -6

Simplifying
t = -6
Subproblem 2
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
Solution
t = {-6, -3}