x(4x+21)+27=0

Solution for x(4x+21)+27=0 equation:

Simplifying
x(4x + 21) + 27 = 0

Reorder the terms:
x(21 + 4x) + 27 = 0
(21 * x + 4x * x) + 27 = 0
(21x + 4x2) + 27 = 0

Reorder the terms:
27 + 21x + 4x2 = 0

Solving
27 + 21x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + x)(9 + 4x) = 0

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(9 + 4x)' equal to zero and attempt to solve:

Simplifying
9 + 4x = 0

Solving
9 + 4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4x = 0 + -9
4x = 0 + -9

Combine like terms: 0 + -9 = -9
4x = -9

Divide each side by '4'.
x = -2.25

Simplifying
x = -2.25
Solution
x = {-3, -2.25}