2x(x+8)=(x-6)(x+8)

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Solution for 2x(x+8)=(x-6)(x+8) equation: 


Simplifying
2x(x + 8) = (x + -6)(x + 8)

Reorder the terms:
2x(8 + x) = (x + -6)(x + 8)
(8 * 2x + x * 2x) = (x + -6)(x + 8)
(16x + 2x2) = (x + -6)(x + 8)

Reorder the terms:
16x + 2x2 = (-6 + x)(x + 8)

Reorder the terms:
16x + 2x2 = (-6 + x)(8 + x)

Multiply (-6 + x) * (8 + x)
16x + 2x2 = (-6(8 + x) + x(8 + x))
16x + 2x2 = ((8 * -6 + x * -6) + x(8 + x))
16x + 2x2 = ((-48 + -6x) + x(8 + x))
16x + 2x2 = (-48 + -6x + (8 * x + x * x))
16x + 2x2 = (-48 + -6x + (8x + x2))

Combine like terms: -6x + 8x = 2x
16x + 2x2 = (-48 + 2x + x2)

Solving
16x + 2x2 = -48 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
48 + 16x + -2x + 2x2 + -1x2 = -48 + 2x + x2 + 48 + -2x + -1x2

Combine like terms: 16x + -2x = 14x
48 + 14x + 2x2 + -1x2 = -48 + 2x + x2 + 48 + -2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
48 + 14x + 1x2 = -48 + 2x + x2 + 48 + -2x + -1x2

Reorder the terms:
48 + 14x + 1x2 = -48 + 48 + 2x + -2x + x2 + -1x2

Combine like terms: -48 + 48 = 0
48 + 14x + 1x2 = 0 + 2x + -2x + x2 + -1x2
48 + 14x + 1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
48 + 14x + 1x2 = 0 + x2 + -1x2
48 + 14x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
48 + 14x + 1x2 = 0

Factor a trinomial.
(8 + x)(6 + x) = 0


Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {-8, -6}

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