5a^2=-5+10a

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

Simplifying
5a2 = -5 + 10a

Solving
5a2 = -5 + 10a

Solving for variable 'a'.

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

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

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

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

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

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

Ignore the factor 5.
Subproblem 1
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
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}