t+45=t(t-3)

Solution for t+45=t(t-3) equation:

Simplifying
t + 45 = t(t + -3)

Reorder the terms:
45 + t = t(t + -3)

Reorder the terms:
45 + t = t(-3 + t)
45 + t = (-3 * t + t * t)
45 + t = (-3t + t2)

Solving
45 + t = -3t + t2

Solving for variable 't'.

Combine like terms: t + 3t = 4t
45 + 4t + -1t2 = -3t + t2 + 3t + -1t2

Reorder the terms:
45 + 4t + -1t2 = -3t + 3t + t2 + -1t2

Combine like terms: -3t + 3t = 0
45 + 4t + -1t2 = 0 + t2 + -1t2
45 + 4t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
45 + 4t + -1t2 = 0

Factor a trinomial.
(9 + -1t)(5 + t) = 0

Subproblem 1
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
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 = {9, -5}