6t^2+19t-7=0

Solution for 6t^2+19t-7=0 equation:

Simplifying
6t2 + 19t + -7 = 0

Reorder the terms:
-7 + 19t + 6t2 = 0

Solving
-7 + 19t + 6t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-7 + -2t)(1 + -3t) = 0

Subproblem 1
Set the factor '(-7 + -2t)' equal to zero and attempt to solve:

Simplifying
-7 + -2t = 0

Solving
-7 + -2t = 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 + -2t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2t = 0 + 7
-2t = 0 + 7

Combine like terms: 0 + 7 = 7
-2t = 7

Divide each side by '-2'.
t = -3.5

Simplifying
t = -3.5
Subproblem 2
Set the factor '(1 + -3t)' equal to zero and attempt to solve:

Simplifying
1 + -3t = 0

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

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

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

Divide each side by '-3'.
t = 0.3333333333

Simplifying
t = 0.3333333333
Solution
t = {-3.5, 0.3333333333}