10=5t^2+5t

Solution for 10=5t^2+5t equation:

Simplifying
10 = 5t2 + 5t

Reorder the terms:
10 = 5t + 5t2

Solving
10 = 5t + 5t2

Solving for variable 't'.

Reorder the terms:
10 + -5t + -5t2 = 5t + -5t + 5t2 + -5t2

Combine like terms: 5t + -5t = 0
10 + -5t + -5t2 = 0 + 5t2 + -5t2
10 + -5t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
10 + -5t + -5t2 = 0

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

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

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

Simplifying
2 + t = 0

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

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

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

Simplifying
t = -2
Solution
t = {1, -2}