-5a^2+10a-16=-11

Solution for -5a^2+10a-16=-11 equation:

Simplifying
-5a2 + 10a + -16 = -11

Reorder the terms:
-16 + 10a + -5a2 = -11

Solving
-16 + 10a + -5a2 = -11

Solving for variable 'a'.

Reorder the terms:
-16 + 11 + 10a + -5a2 = -11 + 11

Combine like terms: -16 + 11 = -5
-5 + 10a + -5a2 = -11 + 11

Combine like terms: -11 + 11 = 0
-5 + 10a + -5a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 2a + -1a2) = 0

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

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + a)' equal to zero and attempt to solve:

Simplifying
-1 + a = 0

Solving
-1 + a = 0

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

Add '1' to each side of the equation.
-1 + 1 + a = 0 + 1

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

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

Simplifying
a = 1
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1a = 0 + -1

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

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

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Solution
a = {1, 1}