t*t+2t-48=15

Solution for t*t+2t-48=15 equation:

Simplifying
t * t + 2t + -48 = 15

Multiply t * t
t2 + 2t + -48 = 15

Reorder the terms:
-48 + 2t + t2 = 15

Solving
-48 + 2t + t2 = 15

Solving for variable 't'.

Reorder the terms:
-48 + -15 + 2t + t2 = 15 + -15

Combine like terms: -48 + -15 = -63
-63 + 2t + t2 = 15 + -15

Combine like terms: 15 + -15 = 0
-63 + 2t + t2 = 0

Factor a trinomial.
(-9 + -1t)(7 + -1t) = 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 '(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 = {-9, 7}