=(2t-3)(t+5)

Solution for =(2t-3)(t+5) equation:

Simplifying
0 = (2t + -3)(t + 5)

Reorder the terms:
0 = (-3 + 2t)(t + 5)

Reorder the terms:
0 = (-3 + 2t)(5 + t)

Multiply (-3 + 2t) * (5 + t)
0 = (-3(5 + t) + 2t * (5 + t))
0 = ((5 * -3 + t * -3) + 2t * (5 + t))
0 = ((-15 + -3t) + 2t * (5 + t))
0 = (-15 + -3t + (5 * 2t + t * 2t))
0 = (-15 + -3t + (10t + 2t2))

Combine like terms: -3t + 10t = 7t
0 = (-15 + 7t + 2t2)

Solving
0 = -15 + 7t + 2t2

Solving for variable 't'.

Combine like terms: 0 + 15 = 15
15 + -7t + -2t2 = -15 + 7t + 2t2 + 15 + -7t + -2t2

Reorder the terms:
15 + -7t + -2t2 = -15 + 15 + 7t + -7t + 2t2 + -2t2

Combine like terms: -15 + 15 = 0
15 + -7t + -2t2 = 0 + 7t + -7t + 2t2 + -2t2
15 + -7t + -2t2 = 7t + -7t + 2t2 + -2t2

Combine like terms: 7t + -7t = 0
15 + -7t + -2t2 = 0 + 2t2 + -2t2
15 + -7t + -2t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
15 + -7t + -2t2 = 0

Factor a trinomial.
(3 + -2t)(5 + t) = 0

Subproblem 1
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 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 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Subproblem 2
Set the factor '(5 + t)' equal to zero and attempt to solve:

Simplifying
5 + t = 0

Solving
5 + t = 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 + t = 0 + -5

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

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

Simplifying
t = -5
Solution
t = {1.5, -5}