(t+4)(t-3)=18

Solution for (t+4)(t-3)=18 equation:

Simplifying
(t + 4)(t + -3) = 18

Reorder the terms:
(4 + t)(t + -3) = 18

Reorder the terms:
(4 + t)(-3 + t) = 18

Multiply (4 + t) * (-3 + t)
(4(-3 + t) + t(-3 + t)) = 18
((-3 * 4 + t * 4) + t(-3 + t)) = 18
((-12 + 4t) + t(-3 + t)) = 18
(-12 + 4t + (-3 * t + t * t)) = 18
(-12 + 4t + (-3t + t2)) = 18

Combine like terms: 4t + -3t = 1t
(-12 + 1t + t2) = 18

Solving
-12 + 1t + t2 = 18

Solving for variable 't'.

Reorder the terms:
-12 + -18 + 1t + t2 = 18 + -18

Combine like terms: -12 + -18 = -30
-30 + 1t + t2 = 18 + -18

Combine like terms: 18 + -18 = 0
-30 + 1t + t2 = 0

Factor a trinomial.
(-6 + -1t)(5 + -1t) = 0

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

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 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 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-6, 5}