(x+3)(x-7)=(8x+17)+(7-8x)

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Solution for (x+3)(x-7)=(8x+17)+(7-8x) equation: 


Simplifying
(x + 3)(x + -7) = (8x + 17) + (7 + -8x)

Reorder the terms:
(3 + x)(x + -7) = (8x + 17) + (7 + -8x)

Reorder the terms:
(3 + x)(-7 + x) = (8x + 17) + (7 + -8x)

Multiply (3 + x) * (-7 + x)
(3(-7 + x) + x(-7 + x)) = (8x + 17) + (7 + -8x)
((-7 * 3 + x * 3) + x(-7 + x)) = (8x + 17) + (7 + -8x)
((-21 + 3x) + x(-7 + x)) = (8x + 17) + (7 + -8x)
(-21 + 3x + (-7 * x + x * x)) = (8x + 17) + (7 + -8x)
(-21 + 3x + (-7x + x2)) = (8x + 17) + (7 + -8x)

Combine like terms: 3x + -7x = -4x
(-21 + -4x + x2) = (8x + 17) + (7 + -8x)

Reorder the terms:
-21 + -4x + x2 = (17 + 8x) + (7 + -8x)

Remove parenthesis around (17 + 8x)
-21 + -4x + x2 = 17 + 8x + (7 + -8x)

Remove parenthesis around (7 + -8x)
-21 + -4x + x2 = 17 + 8x + 7 + -8x

Reorder the terms:
-21 + -4x + x2 = 17 + 7 + 8x + -8x

Combine like terms: 17 + 7 = 24
-21 + -4x + x2 = 24 + 8x + -8x

Combine like terms: 8x + -8x = 0
-21 + -4x + x2 = 24 + 0
-21 + -4x + x2 = 24

Solving
-21 + -4x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
-21 + -24 + -4x + x2 = 24 + -24

Combine like terms: -21 + -24 = -45
-45 + -4x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-45 + -4x + x2 = 0

Factor a trinomial.
(-5 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-5, 9}

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