6t^2=t+7

Solution for 6t^2=t+7 equation:

Simplifying
6t2 = t + 7

Reorder the terms:
6t2 = 7 + t

Solving
6t2 = 7 + t

Solving for variable 't'.

Reorder the terms:
-7 + -1t + 6t2 = 7 + t + -7 + -1t

Reorder the terms:
-7 + -1t + 6t2 = 7 + -7 + t + -1t

Combine like terms: 7 + -7 = 0
-7 + -1t + 6t2 = 0 + t + -1t
-7 + -1t + 6t2 = t + -1t

Combine like terms: t + -1t = 0
-7 + -1t + 6t2 = 0

Factor a trinomial.
(-1 + -1t)(7 + -6t) = 0

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 '(7 + -6t)' equal to zero and attempt to solve:

Simplifying
7 + -6t = 0

Solving
7 + -6t = 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 + -6t = 0 + -7

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

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

Divide each side by '-6'.
t = 1.166666667

Simplifying
t = 1.166666667
Solution
t = {-1, 1.166666667}