6a^2=18a+24

Solution for 6a^2=18a+24 equation:

Simplifying
6a2 = 18a + 24

Reorder the terms:
6a2 = 24 + 18a

Solving
6a2 = 24 + 18a

Solving for variable 'a'.

Reorder the terms:
-24 + -18a + 6a2 = 24 + 18a + -24 + -18a

Reorder the terms:
-24 + -18a + 6a2 = 24 + -24 + 18a + -18a

Combine like terms: 24 + -24 = 0
-24 + -18a + 6a2 = 0 + 18a + -18a
-24 + -18a + 6a2 = 18a + -18a

Combine like terms: 18a + -18a = 0
-24 + -18a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + -3a + a2) = 0

Factor a trinomial.
6((-1 + -1a)(4 + -1a)) = 0

Ignore the factor 6.
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 '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-1, 4}