(x-8)(x-7)-2x(x+3)=8+x

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Solution for (x-8)(x-7)-2x(x+3)=8+x equation: 


Simplifying
(x + -8)(x + -7) + -2x(x + 3) = 8 + x

Reorder the terms:
(-8 + x)(x + -7) + -2x(x + 3) = 8 + x

Reorder the terms:
(-8 + x)(-7 + x) + -2x(x + 3) = 8 + x

Multiply (-8 + x) * (-7 + x)
(-8(-7 + x) + x(-7 + x)) + -2x(x + 3) = 8 + x
((-7 * -8 + x * -8) + x(-7 + x)) + -2x(x + 3) = 8 + x
((56 + -8x) + x(-7 + x)) + -2x(x + 3) = 8 + x
(56 + -8x + (-7 * x + x * x)) + -2x(x + 3) = 8 + x
(56 + -8x + (-7x + x2)) + -2x(x + 3) = 8 + x

Combine like terms: -8x + -7x = -15x
(56 + -15x + x2) + -2x(x + 3) = 8 + x

Reorder the terms:
56 + -15x + x2 + -2x(3 + x) = 8 + x
56 + -15x + x2 + (3 * -2x + x * -2x) = 8 + x
56 + -15x + x2 + (-6x + -2x2) = 8 + x

Reorder the terms:
56 + -15x + -6x + x2 + -2x2 = 8 + x

Combine like terms: -15x + -6x = -21x
56 + -21x + x2 + -2x2 = 8 + x

Combine like terms: x2 + -2x2 = -1x2
56 + -21x + -1x2 = 8 + x

Solving
56 + -21x + -1x2 = 8 + x

Solving for variable 'x'.

Reorder the terms:
56 + -8 + -21x + -1x + -1x2 = 8 + x + -8 + -1x

Combine like terms: 56 + -8 = 48
48 + -21x + -1x + -1x2 = 8 + x + -8 + -1x

Combine like terms: -21x + -1x = -22x
48 + -22x + -1x2 = 8 + x + -8 + -1x

Reorder the terms:
48 + -22x + -1x2 = 8 + -8 + x + -1x

Combine like terms: 8 + -8 = 0
48 + -22x + -1x2 = 0 + x + -1x
48 + -22x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
48 + -22x + -1x2 = 0

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

Simplifying
24 + x = 0

Solving
24 + x = 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 + x = 0 + -24

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

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

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

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