7t^2=6-19t

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

Simplifying
7t2 = 6 + -19t

Solving
7t2 = 6 + -19t

Solving for variable 't'.

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

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

Combine like terms: 6 + -6 = 0
-6 + 19t + 7t2 = 0 + -19t + 19t
-6 + 19t + 7t2 = -19t + 19t

Combine like terms: -19t + 19t = 0
-6 + 19t + 7t2 = 0

Factor a trinomial.
(-3 + -1t)(2 + -7t) = 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 '(2 + -7t)' equal to zero and attempt to solve:

Simplifying
2 + -7t = 0

Solving
2 + -7t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7t = 0 + -2

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

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

Divide each side by '-7'.
t = 0.2857142857

Simplifying
t = 0.2857142857
Solution
t = {-3, 0.2857142857}