4a^2+2a-72=0

Solution for 4a^2+2a-72=0 equation:

Simplifying
4a2 + 2a + -72 = 0

Reorder the terms:
-72 + 2a + 4a2 = 0

Solving
-72 + 2a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + a + 2a2) = 0

Factor a trinomial.
2((-9 + -2a)(4 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -2a)' equal to zero and attempt to solve:

Simplifying
-9 + -2a = 0

Solving
-9 + -2a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2a = 0 + 9
-2a = 0 + 9

Combine like terms: 0 + 9 = 9
-2a = 9

Divide each side by '-2'.
a = -4.5

Simplifying
a = -4.5
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 = {-4.5, 4}