4t^2-37t+75=0

Solution for 4t^2-37t+75=0 equation:

Simplifying
4t2 + -37t + 75 = 0

Reorder the terms:
75 + -37t + 4t2 = 0

Solving
75 + -37t + 4t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + -1t)(25 + -4t) = 0

Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Subproblem 2
Set the factor '(25 + -4t)' equal to zero and attempt to solve:

Simplifying
25 + -4t = 0

Solving
25 + -4t = 0

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

Add '-25' to each side of the equation.
25 + -25 + -4t = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -4t = 0 + -25
-4t = 0 + -25

Combine like terms: 0 + -25 = -25
-4t = -25

Divide each side by '-4'.
t = 6.25

Simplifying
t = 6.25
Solution
t = {3, 6.25}