2T^2-7T-4=0

Solution for 2T^2-7T-4=0 equation:

Simplifying
2T2 + -7T + -4 = 0

Reorder the terms:
-4 + -7T + 2T2 = 0

Solving
-4 + -7T + 2T2 = 0

Solving for variable 'T'.

Factor a trinomial.
(-1 + -2T)(4 + -1T) = 0

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

Simplifying
-1 + -2T = 0

Solving
-1 + -2T = 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 + -2T = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2T = 0 + 1
-2T = 0 + 1

Combine like terms: 0 + 1 = 1
-2T = 1

Divide each side by '-2'.
T = -0.5

Simplifying
T = -0.5
Subproblem 2
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
Solution
T = {-0.5, 4}