(6a-1)(5a+21)=0

Solution for (6a-1)(5a+21)=0 equation:

Simplifying
(6a + -1)(5a + 21) = 0

Reorder the terms:
(-1 + 6a)(5a + 21) = 0

Reorder the terms:
(-1 + 6a)(21 + 5a) = 0

Multiply (-1 + 6a) * (21 + 5a)
(-1(21 + 5a) + 6a * (21 + 5a)) = 0
((21 * -1 + 5a * -1) + 6a * (21 + 5a)) = 0
((-21 + -5a) + 6a * (21 + 5a)) = 0
(-21 + -5a + (21 * 6a + 5a * 6a)) = 0
(-21 + -5a + (126a + 30a2)) = 0

Combine like terms: -5a + 126a = 121a
(-21 + 121a + 30a2) = 0

Solving
-21 + 121a + 30a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-21 + -5a)(1 + -6a) = 0

Subproblem 1
Set the factor '(-21 + -5a)' equal to zero and attempt to solve:

Simplifying
-21 + -5a = 0

Solving
-21 + -5a = 0

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

Add '21' to each side of the equation.
-21 + 21 + -5a = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -5a = 0 + 21
-5a = 0 + 21

Combine like terms: 0 + 21 = 21
-5a = 21

Divide each side by '-5'.
a = -4.2

Simplifying
a = -4.2
Subproblem 2
Set the factor '(1 + -6a)' equal to zero and attempt to solve:

Simplifying
1 + -6a = 0

Solving
1 + -6a = 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 + -6a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6a = 0 + -1
-6a = 0 + -1

Combine like terms: 0 + -1 = -1
-6a = -1

Divide each side by '-6'.
a = 0.1666666667

Simplifying
a = 0.1666666667
Solution
a = {-4.2, 0.1666666667}