6a(a+3)=21-3(1-2a)

Solution for 6a(a+3)=21-3(1-2a) equation:

Simplifying
6a(a + 3) = 21 + -3(1 + -2a)

Reorder the terms:
6a(3 + a) = 21 + -3(1 + -2a)
(3 * 6a + a * 6a) = 21 + -3(1 + -2a)
(18a + 6a2) = 21 + -3(1 + -2a)
18a + 6a2 = 21 + (1 * -3 + -2a * -3)
18a + 6a2 = 21 + (-3 + 6a)

Combine like terms: 21 + -3 = 18
18a + 6a2 = 18 + 6a

Solving
18a + 6a2 = 18 + 6a

Solving for variable 'a'.

Reorder the terms:
-18 + 18a + -6a + 6a2 = 18 + 6a + -18 + -6a

Combine like terms: 18a + -6a = 12a
-18 + 12a + 6a2 = 18 + 6a + -18 + -6a

Reorder the terms:
-18 + 12a + 6a2 = 18 + -18 + 6a + -6a

Combine like terms: 18 + -18 = 0
-18 + 12a + 6a2 = 0 + 6a + -6a
-18 + 12a + 6a2 = 6a + -6a

Combine like terms: 6a + -6a = 0
-18 + 12a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + 2a + a2) = 0

Factor a trinomial.
6((-3 + -1a)(1 + -1a)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a = 0 + 3
-1a = 0 + 3

Combine like terms: 0 + 3 = 3
-1a = 3

Divide each side by '-1'.
a = -3

Simplifying
a = -3
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 = {-3, 1}