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

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Solution for 14(x-4)-(x+2)=(x+2)(x-4) equation: 


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

Reorder the terms:
14(-4 + x) + -1(x + 2) = (x + 2)(x + -4)
(-4 * 14 + x * 14) + -1(x + 2) = (x + 2)(x + -4)
(-56 + 14x) + -1(x + 2) = (x + 2)(x + -4)

Reorder the terms:
-56 + 14x + -1(2 + x) = (x + 2)(x + -4)
-56 + 14x + (2 * -1 + x * -1) = (x + 2)(x + -4)
-56 + 14x + (-2 + -1x) = (x + 2)(x + -4)

Reorder the terms:
-56 + -2 + 14x + -1x = (x + 2)(x + -4)

Combine like terms: -56 + -2 = -58
-58 + 14x + -1x = (x + 2)(x + -4)

Combine like terms: 14x + -1x = 13x
-58 + 13x = (x + 2)(x + -4)

Reorder the terms:
-58 + 13x = (2 + x)(x + -4)

Reorder the terms:
-58 + 13x = (2 + x)(-4 + x)

Multiply (2 + x) * (-4 + x)
-58 + 13x = (2(-4 + x) + x(-4 + x))
-58 + 13x = ((-4 * 2 + x * 2) + x(-4 + x))
-58 + 13x = ((-8 + 2x) + x(-4 + x))
-58 + 13x = (-8 + 2x + (-4 * x + x * x))
-58 + 13x = (-8 + 2x + (-4x + x2))

Combine like terms: 2x + -4x = -2x
-58 + 13x = (-8 + -2x + x2)

Solving
-58 + 13x = -8 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-58 + 8 + 13x + 2x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: -58 + 8 = -50
-50 + 13x + 2x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: 13x + 2x = 15x
-50 + 15x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Reorder the terms:
-50 + 15x + -1x2 = -8 + 8 + -2x + 2x + x2 + -1x2

Combine like terms: -8 + 8 = 0
-50 + 15x + -1x2 = 0 + -2x + 2x + x2 + -1x2
-50 + 15x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
-50 + 15x + -1x2 = 0 + x2 + -1x2
-50 + 15x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-50 + 15x + -1x2 = 0

Factor a trinomial.
(-10 + x)(5 + -1x) = 0


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

Simplifying
-10 + x = 0

Solving
-10 + x = 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 + x = 0 + 10

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

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

Simplifying
x = 10

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {10, 5}

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