(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) + -1(x + -7)(3x + 1) = 84

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

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

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

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

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

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

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

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

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

Combine like terms: 85 + 7 = 92
92 + -27x + 20x + 2x2 + -3x2 = 84

Combine like terms: -27x + 20x = -7x
92 + -7x + 2x2 + -3x2 = 84

Combine like terms: 2x2 + -3x2 = -1x2
92 + -7x + -1x2 = 84

Solving
92 + -7x + -1x2 = 84

Solving for variable 'x'.

Reorder the terms:
92 + -84 + -7x + -1x2 = 84 + -84

Combine like terms: 92 + -84 = 8
8 + -7x + -1x2 = 84 + -84

Combine like terms: 84 + -84 = 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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