t^2+4t-50=-3t+10

Solution for t^2+4t-50=-3t+10 equation:

Simplifying
t2 + 4t + -50 = -3t + 10

Reorder the terms:
-50 + 4t + t2 = -3t + 10

Reorder the terms:
-50 + 4t + t2 = 10 + -3t

Solving
-50 + 4t + t2 = 10 + -3t

Solving for variable 't'.

Reorder the terms:
-50 + -10 + 4t + 3t + t2 = 10 + -3t + -10 + 3t

Combine like terms: -50 + -10 = -60
-60 + 4t + 3t + t2 = 10 + -3t + -10 + 3t

Combine like terms: 4t + 3t = 7t
-60 + 7t + t2 = 10 + -3t + -10 + 3t

Reorder the terms:
-60 + 7t + t2 = 10 + -10 + -3t + 3t

Combine like terms: 10 + -10 = 0
-60 + 7t + t2 = 0 + -3t + 3t
-60 + 7t + t2 = -3t + 3t

Combine like terms: -3t + 3t = 0
-60 + 7t + t2 = 0

Factor a trinomial.
(-12 + -1t)(5 + -1t) = 0

Subproblem 1
Set the factor '(-12 + -1t)' equal to zero and attempt to solve:

Simplifying
-12 + -1t = 0

Solving
-12 + -1t = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1t = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1t = 0 + 12
-1t = 0 + 12

Combine like terms: 0 + 12 = 12
-1t = 12

Divide each side by '-1'.
t = -12

Simplifying
t = -12
Subproblem 2
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
Solution
t = {-12, 5}