x(2x+19)+45=0

Solution for x(2x+19)+45=0 equation:

Simplifying
x(2x + 19) + 45 = 0

Reorder the terms:
x(19 + 2x) + 45 = 0
(19 * x + 2x * x) + 45 = 0
(19x + 2x2) + 45 = 0

Reorder the terms:
45 + 19x + 2x2 = 0

Solving
45 + 19x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + x)(9 + 2x) = 0

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

Simplifying
5 + x = 0

Solving
5 + x = 0

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

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

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(9 + 2x)' equal to zero and attempt to solve:

Simplifying
9 + 2x = 0

Solving
9 + 2x = 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 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9

Combine like terms: 0 + -9 = -9
2x = -9

Divide each side by '2'.
x = -4.5

Simplifying
x = -4.5
Solution
x = {-5, -4.5}