8t^2+38t=10

Solution for 8t^2+38t=10 equation:

Simplifying
8t2 + 38t = 10

Reorder the terms:
38t + 8t2 = 10

Solving
38t + 8t2 = 10

Solving for variable 't'.

Reorder the terms:
-10 + 38t + 8t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 38t + 8t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 19t + 4t2) = 0

Factor a trinomial.
2((-5 + -1t)(1 + -4t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve:

Simplifying
-5 + -1t = 0

Solving
-5 + -1t = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1t = 0 + 5
-1t = 0 + 5

Combine like terms: 0 + 5 = 5
-1t = 5

Divide each side by '-1'.
t = -5

Simplifying
t = -5
Subproblem 2
Set the factor '(1 + -4t)' equal to zero and attempt to solve:

Simplifying
1 + -4t = 0

Solving
1 + -4t = 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 + -4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4t = 0 + -1
-4t = 0 + -1

Combine like terms: 0 + -1 = -1
-4t = -1

Divide each side by '-4'.
t = 0.25

Simplifying
t = 0.25
Solution
t = {-5, 0.25}