100T^2-50T-150=0

Solution for 100T^2-50T-150=0 equation:

Simplifying
100T2 + -50T + -150 = 0

Reorder the terms:
-150 + -50T + 100T2 = 0

Solving
-150 + -50T + 100T2 = 0

Solving for variable 'T'.

Factor out the Greatest Common Factor (GCF), '50'.
50(-3 + -1T + 2T2) = 0

Factor a trinomial.
50((-1 + -1T)(3 + -2T)) = 0

Ignore the factor 50.
Subproblem 1
Set the factor '(-1 + -1T)' equal to zero and attempt to solve:

Simplifying
-1 + -1T = 0

Solving
-1 + -1T = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1T = 0 + 1
-1T = 0 + 1

Combine like terms: 0 + 1 = 1
-1T = 1

Divide each side by '-1'.
T = -1

Simplifying
T = -1
Subproblem 2
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
Solution
T = {-1, 1.5}