9t^2=t^2+2t+10

Solution for 9t^2=t^2+2t+10 equation:

Simplifying
9t2 = t2 + 2t + 10

Reorder the terms:
9t2 = 10 + 2t + t2

Solving
9t2 = 10 + 2t + t2

Solving for variable 't'.

Reorder the terms:
-10 + -2t + 9t2 + -1t2 = 10 + 2t + t2 + -10 + -2t + -1t2

Combine like terms: 9t2 + -1t2 = 8t2
-10 + -2t + 8t2 = 10 + 2t + t2 + -10 + -2t + -1t2

Reorder the terms:
-10 + -2t + 8t2 = 10 + -10 + 2t + -2t + t2 + -1t2

Combine like terms: 10 + -10 = 0
-10 + -2t + 8t2 = 0 + 2t + -2t + t2 + -1t2
-10 + -2t + 8t2 = 2t + -2t + t2 + -1t2

Combine like terms: 2t + -2t = 0
-10 + -2t + 8t2 = 0 + t2 + -1t2
-10 + -2t + 8t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-10 + -2t + 8t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -1t + 4t2) = 0

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

Ignore the factor 2.
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 '(5 + -4t)' equal to zero and attempt to solve:

Simplifying
5 + -4t = 0

Solving
5 + -4t = 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 + -4t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4t = 0 + -5
-4t = 0 + -5

Combine like terms: 0 + -5 = -5
-4t = -5

Divide each side by '-4'.
t = 1.25

Simplifying
t = 1.25
Solution
t = {-1, 1.25}