8a^2+53a-21=

Solution for 8a^2+53a-21= equation:

Simplifying
8a2 + 53a + -21 = 0

Reorder the terms:
-21 + 53a + 8a2 = 0

Solving
-21 + 53a + 8a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -1a)(3 + -8a) = 0

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

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 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 + -1a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1a = 0 + 7
-1a = 0 + 7

Combine like terms: 0 + 7 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7
Subproblem 2
Set the factor '(3 + -8a)' equal to zero and attempt to solve:

Simplifying
3 + -8a = 0

Solving
3 + -8a = 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 + -8a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8a = 0 + -3
-8a = 0 + -3

Combine like terms: 0 + -3 = -3
-8a = -3

Divide each side by '-8'.
a = 0.375

Simplifying
a = 0.375
Solution
a = {-7, 0.375}