t^2-3t+2s-23=2s+5

Solution for t^2-3t+2s-23=2s+5 equation:

Simplifying
t2 + -3t + 2s + -23 = 2s + 5

Reorder the terms:
-23 + 2s + -3t + t2 = 2s + 5

Reorder the terms:
-23 + 2s + -3t + t2 = 5 + 2s

Add '-2s' to each side of the equation.
-23 + 2s + -3t + -2s + t2 = 5 + 2s + -2s

Reorder the terms:
-23 + 2s + -2s + -3t + t2 = 5 + 2s + -2s

Combine like terms: 2s + -2s = 0
-23 + 0 + -3t + t2 = 5 + 2s + -2s
-23 + -3t + t2 = 5 + 2s + -2s

Combine like terms: 2s + -2s = 0
-23 + -3t + t2 = 5 + 0
-23 + -3t + t2 = 5

Solving
-23 + -3t + t2 = 5

Solving for variable 't'.

Reorder the terms:
-23 + -5 + -3t + t2 = 5 + -5

Combine like terms: -23 + -5 = -28
-28 + -3t + t2 = 5 + -5

Combine like terms: 5 + -5 = 0
-28 + -3t + t2 = 0

Factor a trinomial.
(-4 + -1t)(7 + -1t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve:

Simplifying
7 + -1t = 0

Solving
7 + -1t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t = 0 + -7
-1t = 0 + -7

Combine like terms: 0 + -7 = -7
-1t = -7

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Solution
t = {-4, 7}