-2t^2+4t+8=10

Solution for -2t^2+4t+8=10 equation:

Simplifying
-2t2 + 4t + 8 = 10

Reorder the terms:
8 + 4t + -2t2 = 10

Solving
8 + 4t + -2t2 = 10

Solving for variable 't'.

Reorder the terms:
8 + -10 + 4t + -2t2 = 10 + -10

Combine like terms: 8 + -10 = -2
-2 + 4t + -2t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-2 + 4t + -2t2 = 0

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

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

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

Simplifying
-1 + t = 0

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

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

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

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