12(x+4)-1(x+4)(x-4)=14(x-4)

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Solution for 12(x+4)-1(x+4)(x-4)=14(x-4) equation: 


Simplifying
12(x + 4) + -1(x + 4)(x + -4) = 14(x + -4)

Reorder the terms:
12(4 + x) + -1(x + 4)(x + -4) = 14(x + -4)
(4 * 12 + x * 12) + -1(x + 4)(x + -4) = 14(x + -4)
(48 + 12x) + -1(x + 4)(x + -4) = 14(x + -4)

Reorder the terms:
48 + 12x + -1(4 + x)(x + -4) = 14(x + -4)

Reorder the terms:
48 + 12x + -1(4 + x)(-4 + x) = 14(x + -4)

Multiply (4 + x) * (-4 + x)
48 + 12x + -1(4(-4 + x) + x(-4 + x)) = 14(x + -4)
48 + 12x + -1((-4 * 4 + x * 4) + x(-4 + x)) = 14(x + -4)
48 + 12x + -1((-16 + 4x) + x(-4 + x)) = 14(x + -4)
48 + 12x + -1(-16 + 4x + (-4 * x + x * x)) = 14(x + -4)
48 + 12x + -1(-16 + 4x + (-4x + x2)) = 14(x + -4)

Combine like terms: 4x + -4x = 0
48 + 12x + -1(-16 + 0 + x2) = 14(x + -4)
48 + 12x + -1(-16 + x2) = 14(x + -4)
48 + 12x + (-16 * -1 + x2 * -1) = 14(x + -4)
48 + 12x + (16 + -1x2) = 14(x + -4)

Reorder the terms:
48 + 16 + 12x + -1x2 = 14(x + -4)

Combine like terms: 48 + 16 = 64
64 + 12x + -1x2 = 14(x + -4)

Reorder the terms:
64 + 12x + -1x2 = 14(-4 + x)
64 + 12x + -1x2 = (-4 * 14 + x * 14)
64 + 12x + -1x2 = (-56 + 14x)

Solving
64 + 12x + -1x2 = -56 + 14x

Solving for variable 'x'.

Reorder the terms:
64 + 56 + 12x + -14x + -1x2 = -56 + 14x + 56 + -14x

Combine like terms: 64 + 56 = 120
120 + 12x + -14x + -1x2 = -56 + 14x + 56 + -14x

Combine like terms: 12x + -14x = -2x
120 + -2x + -1x2 = -56 + 14x + 56 + -14x

Reorder the terms:
120 + -2x + -1x2 = -56 + 56 + 14x + -14x

Combine like terms: -56 + 56 = 0
120 + -2x + -1x2 = 0 + 14x + -14x
120 + -2x + -1x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
120 + -2x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(12 + x) = 0


Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10

Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {10, -12}

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