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

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


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

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

Multiply (4 + x) * (4 + -1x)
(4(4 + -1x) + x(4 + -1x)) = 3(3x + -2)
((4 * 4 + -1x * 4) + x(4 + -1x)) = 3(3x + -2)
((16 + -4x) + x(4 + -1x)) = 3(3x + -2)
(16 + -4x + (4 * x + -1x * x)) = 3(3x + -2)
(16 + -4x + (4x + -1x2)) = 3(3x + -2)

Combine like terms: -4x + 4x = 0
(16 + 0 + -1x2) = 3(3x + -2)
(16 + -1x2) = 3(3x + -2)

Reorder the terms:
16 + -1x2 = 3(-2 + 3x)
16 + -1x2 = (-2 * 3 + 3x * 3)
16 + -1x2 = (-6 + 9x)

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

Solving for variable 'x'.

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

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

Reorder the terms:
22 + -9x + -1x2 = -6 + 6 + 9x + -9x

Combine like terms: -6 + 6 = 0
22 + -9x + -1x2 = 0 + 9x + -9x
22 + -9x + -1x2 = 9x + -9x

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

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


Subproblem 1
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

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

Simplifying
11 + x = 0

Solving
11 + x = 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 + x = 0 + -11

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

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

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

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