3(3x-2)=(x+4)(4-x)

Solution for 3(3x-2)=(x+4)(4-x) equation:

Simplifying
3(3x + -2) = (x + 4)(4 + -1x)

Reorder the terms:
3(-2 + 3x) = (x + 4)(4 + -1x)
(-2 * 3 + 3x * 3) = (x + 4)(4 + -1x)
(-6 + 9x) = (x + 4)(4 + -1x)

Reorder the terms:
-6 + 9x = (4 + x)(4 + -1x)

Multiply (4 + x) * (4 + -1x)
-6 + 9x = (4(4 + -1x) + x(4 + -1x))
-6 + 9x = ((4 * 4 + -1x * 4) + x(4 + -1x))
-6 + 9x = ((16 + -4x) + x(4 + -1x))
-6 + 9x = (16 + -4x + (4 * x + -1x * x))
-6 + 9x = (16 + -4x + (4x + -1x2))

Combine like terms: -4x + 4x = 0
-6 + 9x = (16 + 0 + -1x2)
-6 + 9x = (16 + -1x2)

Solving
-6 + 9x = 16 + -1x2

Solving for variable 'x'.

Reorder the terms:
-6 + -16 + 9x + x2 = 16 + -1x2 + -16 + x2

Combine like terms: -6 + -16 = -22
-22 + 9x + x2 = 16 + -1x2 + -16 + x2

Reorder the terms:
-22 + 9x + x2 = 16 + -16 + -1x2 + x2

Combine like terms: 16 + -16 = 0
-22 + 9x + x2 = 0 + -1x2 + x2
-22 + 9x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-22 + 9x + x2 = 0

Factor a trinomial.
(-11 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-11, 2}