(t-5)(t+4)=52

Solution for (t-5)(t+4)=52 equation:

Simplifying
(t + -5)(t + 4) = 52

Reorder the terms:
(-5 + t)(t + 4) = 52

Reorder the terms:
(-5 + t)(4 + t) = 52

Multiply (-5 + t) * (4 + t)
(-5(4 + t) + t(4 + t)) = 52
((4 * -5 + t * -5) + t(4 + t)) = 52
((-20 + -5t) + t(4 + t)) = 52
(-20 + -5t + (4 * t + t * t)) = 52
(-20 + -5t + (4t + t2)) = 52

Combine like terms: -5t + 4t = -1t
(-20 + -1t + t2) = 52

Solving
-20 + -1t + t2 = 52

Solving for variable 't'.

Reorder the terms:
-20 + -52 + -1t + t2 = 52 + -52

Combine like terms: -20 + -52 = -72
-72 + -1t + t2 = 52 + -52

Combine like terms: 52 + -52 = 0
-72 + -1t + t2 = 0

Factor a trinomial.
(-8 + -1t)(9 + -1t) = 0

Subproblem 1
Set the factor '(-8 + -1t)' equal to zero and attempt to solve:

Simplifying
-8 + -1t = 0

Solving
-8 + -1t = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1t = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1t = 0 + 8
-1t = 0 + 8

Combine like terms: 0 + 8 = 8
-1t = 8

Divide each side by '-1'.
t = -8

Simplifying
t = -8
Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

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

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

Divide each side by '-1'.
t = 9

Simplifying
t = 9
Solution
t = {-8, 9}