10a(a+1)=2(a+2)-2

Solution for 10a(a+1)=2(a+2)-2 equation:

Simplifying
10a(a + 1) = 2(a + 2) + -2

Reorder the terms:
10a(1 + a) = 2(a + 2) + -2
(1 * 10a + a * 10a) = 2(a + 2) + -2
(10a + 10a2) = 2(a + 2) + -2

Reorder the terms:
10a + 10a2 = 2(2 + a) + -2
10a + 10a2 = (2 * 2 + a * 2) + -2
10a + 10a2 = (4 + 2a) + -2

Reorder the terms:
10a + 10a2 = 4 + -2 + 2a

Combine like terms: 4 + -2 = 2
10a + 10a2 = 2 + 2a

Solving
10a + 10a2 = 2 + 2a

Solving for variable 'a'.

Reorder the terms:
-2 + 10a + -2a + 10a2 = 2 + 2a + -2 + -2a

Combine like terms: 10a + -2a = 8a
-2 + 8a + 10a2 = 2 + 2a + -2 + -2a

Reorder the terms:
-2 + 8a + 10a2 = 2 + -2 + 2a + -2a

Combine like terms: 2 + -2 = 0
-2 + 8a + 10a2 = 0 + 2a + -2a
-2 + 8a + 10a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
-2 + 8a + 10a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 4a + 5a2) = 0

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

Ignore the factor 2.
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 + -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
Solution
a = {-1, 0.2}