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

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

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

Reorder the terms:
2x(-4 + x) = 9x + 9
(-4 * 2x + x * 2x) = 9x + 9
(-8x + 2x2) = 9x + 9

Reorder the terms:
-8x + 2x2 = 9 + 9x

Solving
-8x + 2x2 = 9 + 9x

Solving for variable 'x'.

Reorder the terms:
-9 + -8x + -9x + 2x2 = 9 + 9x + -9 + -9x

Combine like terms: -8x + -9x = -17x
-9 + -17x + 2x2 = 9 + 9x + -9 + -9x

Reorder the terms:
-9 + -17x + 2x2 = 9 + -9 + 9x + -9x

Combine like terms: 9 + -9 = 0
-9 + -17x + 2x2 = 0 + 9x + -9x
-9 + -17x + 2x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-9 + -17x + 2x2 = 0

Factor a trinomial.
(-1 + -2x)(9 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-0.5, 9}