25a^2=20a+5

Solution for 25a^2=20a+5 equation:

Simplifying
25a2 = 20a + 5

Reorder the terms:
25a2 = 5 + 20a

Solving
25a2 = 5 + 20a

Solving for variable 'a'.

Reorder the terms:
-5 + -20a + 25a2 = 5 + 20a + -5 + -20a

Reorder the terms:
-5 + -20a + 25a2 = 5 + -5 + 20a + -20a

Combine like terms: 5 + -5 = 0
-5 + -20a + 25a2 = 0 + 20a + -20a
-5 + -20a + 25a2 = 20a + -20a

Combine like terms: 20a + -20a = 0
-5 + -20a + 25a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + -4a + 5a2) = 0

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

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

Simplifying
-1 + -5a = 0

Solving
-1 + -5a = 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 + -5a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5a = 0 + 1
-5a = 0 + 1

Combine like terms: 0 + 1 = 1
-5a = 1

Divide each side by '-5'.
a = -0.2

Simplifying
a = -0.2
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 = {-0.2, 1}