27x^2+48x+21=0

Solution for 27x^2+48x+21=0 equation:

Simplifying
27x2 + 48x + 21 = 0

Reorder the terms:
21 + 48x + 27x2 = 0

Solving
21 + 48x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + 16x + 9x2) = 0

Factor a trinomial.
3((1 + x)(7 + 9x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Subproblem 2
Set the factor '(7 + 9x)' equal to zero and attempt to solve:

Simplifying
7 + 9x = 0

Solving
7 + 9x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 9x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 9x = 0 + -7
9x = 0 + -7

Combine like terms: 0 + -7 = -7
9x = -7

Divide each side by '9'.
x = -0.7777777778

Simplifying
x = -0.7777777778
Solution
x = {-1, -0.7777777778}