21a^2+5a-4=0

Solution for 21a^2+5a-4=0 equation:

Simplifying
21a2 + 5a + -4 = 0

Reorder the terms:
-4 + 5a + 21a2 = 0

Solving
-4 + 5a + 21a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-4 + -7a)(1 + -3a) = 0

Subproblem 1
Set the factor '(-4 + -7a)' equal to zero and attempt to solve:

Simplifying
-4 + -7a = 0

Solving
-4 + -7a = 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 + -7a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -7a = 0 + 4
-7a = 0 + 4

Combine like terms: 0 + 4 = 4
-7a = 4

Divide each side by '-7'.
a = -0.5714285714

Simplifying
a = -0.5714285714
Subproblem 2
Set the factor '(1 + -3a)' equal to zero and attempt to solve:

Simplifying
1 + -3a = 0

Solving
1 + -3a = 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 + -3a = 0 + -1

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

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

Divide each side by '-3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
Solution
a = {-0.5714285714, 0.3333333333}