t(9+t)=4(2t+5)

Solution for t(9+t)=4(2t+5) equation:

Simplifying
t(9 + t) = 4(2t + 5)
(9 * t + t * t) = 4(2t + 5)
(9t + t2) = 4(2t + 5)

Reorder the terms:
9t + t2 = 4(5 + 2t)
9t + t2 = (5 * 4 + 2t * 4)
9t + t2 = (20 + 8t)

Solving
9t + t2 = 20 + 8t

Solving for variable 't'.

Reorder the terms:
-20 + 9t + -8t + t2 = 20 + 8t + -20 + -8t

Combine like terms: 9t + -8t = 1t
-20 + 1t + t2 = 20 + 8t + -20 + -8t

Reorder the terms:
-20 + 1t + t2 = 20 + -20 + 8t + -8t

Combine like terms: 20 + -20 = 0
-20 + 1t + t2 = 0 + 8t + -8t
-20 + 1t + t2 = 8t + -8t

Combine like terms: 8t + -8t = 0
-20 + 1t + t2 = 0

Factor a trinomial.
(-5 + -1t)(4 + -1t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

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

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

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-5, 4}