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

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


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

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

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

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

Combine like terms: 4x + -12x = -8x
(-48 + -8x + x2) = 14x

Solving
-48 + -8x + x2 = 14x

Solving for variable 'x'.

Reorder the terms:
-48 + -8x + -14x + x2 = 14x + -14x

Combine like terms: -8x + -14x = -22x
-48 + -22x + x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-48 + -22x + x2 = 0

Factor a trinomial.
(-2 + -1x)(24 + -1x) = 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 '(24 + -1x)' equal to zero and attempt to solve:

Simplifying
24 + -1x = 0

Solving
24 + -1x = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1x = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1x = 0 + -24
-1x = 0 + -24

Combine like terms: 0 + -24 = -24
-1x = -24

Divide each side by '-1'.
x = 24

Simplifying
x = 24
Solution
x = {-2, 24}

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