(2x+1)*(x-5)+18x=0

Solution for (2x+1)*(x-5)+18x=0 equation:

Simplifying
(2x + 1)(x + -5) + 18x = 0

Reorder the terms:
(1 + 2x)(x + -5) + 18x = 0

Reorder the terms:
(1 + 2x)(-5 + x) + 18x = 0

Multiply (1 + 2x) * (-5 + x)
(1(-5 + x) + 2x * (-5 + x)) + 18x = 0
((-5 * 1 + x * 1) + 2x * (-5 + x)) + 18x = 0
((-5 + 1x) + 2x * (-5 + x)) + 18x = 0
(-5 + 1x + (-5 * 2x + x * 2x)) + 18x = 0
(-5 + 1x + (-10x + 2x2)) + 18x = 0

Combine like terms: 1x + -10x = -9x
(-5 + -9x + 2x2) + 18x = 0

Reorder the terms:
-5 + -9x + 18x + 2x2 = 0

Combine like terms: -9x + 18x = 9x
-5 + 9x + 2x2 = 0

Solving
-5 + 9x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -1x)(1 + -2x) = 0

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-5, 0.5}