4x^2+27x+45=0

Solution for 4x^2+27x+45=0 equation:

Simplifying
4x2 + 27x + 45 = 0

Reorder the terms:
45 + 27x + 4x2 = 0

Solving
45 + 27x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(15 + 4x)(3 + x) = 0

Subproblem 1
Set the factor '(15 + 4x)' equal to zero and attempt to solve:

Simplifying
15 + 4x = 0

Solving
15 + 4x = 0

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

Add '-15' to each side of the equation.
15 + -15 + 4x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 4x = 0 + -15
4x = 0 + -15

Combine like terms: 0 + -15 = -15
4x = -15

Divide each side by '4'.
x = -3.75

Simplifying
x = -3.75
Subproblem 2
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
Solution
x = {-3.75, -3}