5a(a+3)-a=4a-6+1

Solution for 5a(a+3)-a=4a-6+1 equation:

Simplifying
5a(a + 3) + -1a = 4a + -6 + 1

Reorder the terms:
5a(3 + a) + -1a = 4a + -6 + 1
(3 * 5a + a * 5a) + -1a = 4a + -6 + 1
(15a + 5a2) + -1a = 4a + -6 + 1

Reorder the terms:
15a + -1a + 5a2 = 4a + -6 + 1

Combine like terms: 15a + -1a = 14a
14a + 5a2 = 4a + -6 + 1

Reorder the terms:
14a + 5a2 = -6 + 1 + 4a

Combine like terms: -6 + 1 = -5
14a + 5a2 = -5 + 4a

Solving
14a + 5a2 = -5 + 4a

Solving for variable 'a'.

Reorder the terms:
5 + 14a + -4a + 5a2 = -5 + 4a + 5 + -4a

Combine like terms: 14a + -4a = 10a
5 + 10a + 5a2 = -5 + 4a + 5 + -4a

Reorder the terms:
5 + 10a + 5a2 = -5 + 5 + 4a + -4a

Combine like terms: -5 + 5 = 0
5 + 10a + 5a2 = 0 + 4a + -4a
5 + 10a + 5a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
5 + 10a + 5a2 = 0

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

Factor a trinomial.
5((1 + a)(1 + a)) = 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 + 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
Solution
a = {-1, -1}