(2-x)*(x+4)=3x+12

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Solution for (2-x)*(x+4)=3x+12 equation: 


Simplifying
(2 + -1x)(x + 4) = 3x + 12

Reorder the terms:
(2 + -1x)(4 + x) = 3x + 12

Multiply (2 + -1x) * (4 + x)
(2(4 + x) + -1x * (4 + x)) = 3x + 12
((4 * 2 + x * 2) + -1x * (4 + x)) = 3x + 12
((8 + 2x) + -1x * (4 + x)) = 3x + 12
(8 + 2x + (4 * -1x + x * -1x)) = 3x + 12
(8 + 2x + (-4x + -1x2)) = 3x + 12

Combine like terms: 2x + -4x = -2x
(8 + -2x + -1x2) = 3x + 12

Reorder the terms:
8 + -2x + -1x2 = 12 + 3x

Solving
8 + -2x + -1x2 = 12 + 3x

Solving for variable 'x'.

Reorder the terms:
8 + -12 + -2x + -3x + -1x2 = 12 + 3x + -12 + -3x

Combine like terms: 8 + -12 = -4
-4 + -2x + -3x + -1x2 = 12 + 3x + -12 + -3x

Combine like terms: -2x + -3x = -5x
-4 + -5x + -1x2 = 12 + 3x + -12 + -3x

Reorder the terms:
-4 + -5x + -1x2 = 12 + -12 + 3x + -3x

Combine like terms: 12 + -12 = 0
-4 + -5x + -1x2 = 0 + 3x + -3x
-4 + -5x + -1x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-4 + -5x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 5x + x2) = 0

Factor a trinomial.
-1((4 + x)(1 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-4, -1}

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