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

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


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

Multiply (4 + -1x) * (4 + x)
(4(4 + x) + -1x * (4 + x)) + -1x = 2(4x + 3)
((4 * 4 + x * 4) + -1x * (4 + x)) + -1x = 2(4x + 3)
((16 + 4x) + -1x * (4 + x)) + -1x = 2(4x + 3)
(16 + 4x + (4 * -1x + x * -1x)) + -1x = 2(4x + 3)
(16 + 4x + (-4x + -1x2)) + -1x = 2(4x + 3)

Combine like terms: 4x + -4x = 0
(16 + 0 + -1x2) + -1x = 2(4x + 3)
(16 + -1x2) + -1x = 2(4x + 3)

Reorder the terms:
16 + -1x + -1x2 = 2(4x + 3)

Reorder the terms:
16 + -1x + -1x2 = 2(3 + 4x)
16 + -1x + -1x2 = (3 * 2 + 4x * 2)
16 + -1x + -1x2 = (6 + 8x)

Solving
16 + -1x + -1x2 = 6 + 8x

Solving for variable 'x'.

Reorder the terms:
16 + -6 + -1x + -8x + -1x2 = 6 + 8x + -6 + -8x

Combine like terms: 16 + -6 = 10
10 + -1x + -8x + -1x2 = 6 + 8x + -6 + -8x

Combine like terms: -1x + -8x = -9x
10 + -9x + -1x2 = 6 + 8x + -6 + -8x

Reorder the terms:
10 + -9x + -1x2 = 6 + -6 + 8x + -8x

Combine like terms: 6 + -6 = 0
10 + -9x + -1x2 = 0 + 8x + -8x
10 + -9x + -1x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
10 + -9x + -1x2 = 0

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


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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

Subproblem 2
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
Solution
x = {1, -10}

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