0=27a^2+42a-5

Solution for 0=27a^2+42a-5 equation:

Simplifying
0 = 27a2 + 42a + -5

Reorder the terms:
0 = -5 + 42a + 27a2

Solving
0 = -5 + 42a + 27a2

Solving for variable 'a'.

Combine like terms: 0 + 5 = 5
5 + -42a + -27a2 = -5 + 42a + 27a2 + 5 + -42a + -27a2

Reorder the terms:
5 + -42a + -27a2 = -5 + 5 + 42a + -42a + 27a2 + -27a2

Combine like terms: -5 + 5 = 0
5 + -42a + -27a2 = 0 + 42a + -42a + 27a2 + -27a2
5 + -42a + -27a2 = 42a + -42a + 27a2 + -27a2

Combine like terms: 42a + -42a = 0
5 + -42a + -27a2 = 0 + 27a2 + -27a2
5 + -42a + -27a2 = 27a2 + -27a2

Combine like terms: 27a2 + -27a2 = 0
5 + -42a + -27a2 = 0

Factor a trinomial.
(1 + -9a)(5 + 3a) = 0

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

Simplifying
1 + -9a = 0

Solving
1 + -9a = 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 + -9a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -9a = 0 + -1
-9a = 0 + -1

Combine like terms: 0 + -1 = -1
-9a = -1

Divide each side by '-9'.
a = 0.1111111111

Simplifying
a = 0.1111111111
Subproblem 2
Set the factor '(5 + 3a)' equal to zero and attempt to solve:

Simplifying
5 + 3a = 0

Solving
5 + 3a = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3a = 0 + -5
3a = 0 + -5

Combine like terms: 0 + -5 = -5
3a = -5

Divide each side by '3'.
a = -1.666666667

Simplifying
a = -1.666666667
Solution
a = {0.1111111111, -1.666666667}