(x-5)(2x-17)=(x-7)(3x+1)+84

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Solution for (x-5)(2x-17)=(x-7)(3x+1)+84 equation: 


Simplifying
(x + -5)(2x + -17) = (x + -7)(3x + 1) + 84

Reorder the terms:
(-5 + x)(2x + -17) = (x + -7)(3x + 1) + 84

Reorder the terms:
(-5 + x)(-17 + 2x) = (x + -7)(3x + 1) + 84

Multiply (-5 + x) * (-17 + 2x)
(-5(-17 + 2x) + x(-17 + 2x)) = (x + -7)(3x + 1) + 84
((-17 * -5 + 2x * -5) + x(-17 + 2x)) = (x + -7)(3x + 1) + 84
((85 + -10x) + x(-17 + 2x)) = (x + -7)(3x + 1) + 84
(85 + -10x + (-17 * x + 2x * x)) = (x + -7)(3x + 1) + 84
(85 + -10x + (-17x + 2x2)) = (x + -7)(3x + 1) + 84

Combine like terms: -10x + -17x = -27x
(85 + -27x + 2x2) = (x + -7)(3x + 1) + 84

Reorder the terms:
85 + -27x + 2x2 = (-7 + x)(3x + 1) + 84

Reorder the terms:
85 + -27x + 2x2 = (-7 + x)(1 + 3x) + 84

Multiply (-7 + x) * (1 + 3x)
85 + -27x + 2x2 = (-7(1 + 3x) + x(1 + 3x)) + 84
85 + -27x + 2x2 = ((1 * -7 + 3x * -7) + x(1 + 3x)) + 84
85 + -27x + 2x2 = ((-7 + -21x) + x(1 + 3x)) + 84
85 + -27x + 2x2 = (-7 + -21x + (1 * x + 3x * x)) + 84
85 + -27x + 2x2 = (-7 + -21x + (1x + 3x2)) + 84

Combine like terms: -21x + 1x = -20x
85 + -27x + 2x2 = (-7 + -20x + 3x2) + 84

Reorder the terms:
85 + -27x + 2x2 = -7 + 84 + -20x + 3x2

Combine like terms: -7 + 84 = 77
85 + -27x + 2x2 = 77 + -20x + 3x2

Solving
85 + -27x + 2x2 = 77 + -20x + 3x2

Solving for variable 'x'.

Reorder the terms:
85 + -77 + -27x + 20x + 2x2 + -3x2 = 77 + -20x + 3x2 + -77 + 20x + -3x2

Combine like terms: 85 + -77 = 8
8 + -27x + 20x + 2x2 + -3x2 = 77 + -20x + 3x2 + -77 + 20x + -3x2

Combine like terms: -27x + 20x = -7x
8 + -7x + 2x2 + -3x2 = 77 + -20x + 3x2 + -77 + 20x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
8 + -7x + -1x2 = 77 + -20x + 3x2 + -77 + 20x + -3x2

Reorder the terms:
8 + -7x + -1x2 = 77 + -77 + -20x + 20x + 3x2 + -3x2

Combine like terms: 77 + -77 = 0
8 + -7x + -1x2 = 0 + -20x + 20x + 3x2 + -3x2
8 + -7x + -1x2 = -20x + 20x + 3x2 + -3x2

Combine like terms: -20x + 20x = 0
8 + -7x + -1x2 = 0 + 3x2 + -3x2
8 + -7x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
8 + -7x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(8 + 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 '(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
Solution
x = {1, -8}

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