(x-2)(x+9)-4x=0

Solution for (x-2)(x+9)-4x=0 equation:

Simplifying
(x + -2)(x + 9) + -4x = 0

Reorder the terms:
(-2 + x)(x + 9) + -4x = 0

Reorder the terms:
(-2 + x)(9 + x) + -4x = 0

Multiply (-2 + x) * (9 + x)
(-2(9 + x) + x(9 + x)) + -4x = 0
((9 * -2 + x * -2) + x(9 + x)) + -4x = 0
((-18 + -2x) + x(9 + x)) + -4x = 0
(-18 + -2x + (9 * x + x * x)) + -4x = 0
(-18 + -2x + (9x + x2)) + -4x = 0

Combine like terms: -2x + 9x = 7x
(-18 + 7x + x2) + -4x = 0

Reorder the terms:
-18 + 7x + -4x + x2 = 0

Combine like terms: 7x + -4x = 3x
-18 + 3x + x2 = 0

Solving
-18 + 3x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-6, 3}