(4(a^2))+(8a)-21=0

Solution for (4(a^2))+(8a)-21=0 equation:

Simplifying
(4(a2)) + (8a) + -21 = 0

Reorder the terms:
-21 + (8a) + (4a2) = 0

Solving
-21 + (8a) + (4a2) = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -2a)(3 + -2a) = 0

Subproblem 1
Set the factor '(-7 + -2a)' equal to zero and attempt to solve:

Simplifying
-7 + -2a = 0

Solving
-7 + -2a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2a = 0 + 7
-2a = 0 + 7

Combine like terms: 0 + 7 = 7
-2a = 7

Divide each side by '-2'.
a = -3.5

Simplifying
a = -3.5
Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve:

Simplifying
3 + -2a = 0

Solving
3 + -2a = 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 + -2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2a = 0 + -3
-2a = 0 + -3

Combine like terms: 0 + -3 = -3
-2a = -3

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Solution
a = {-3.5, 1.5}