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

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

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

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

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

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

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

Solving
-18 + 7x + x2 = 4x

Solving for variable 'x'.

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

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

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

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}