(X+17)(X-8)=21(X-8)

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Solution for (X+17)(X-8)=21(X-8) equation: 


Simplifying
(X + 17)(X + -8) = 21(X + -8)

Reorder the terms:
(17 + X)(X + -8) = 21(X + -8)

Reorder the terms:
(17 + X)(-8 + X) = 21(X + -8)

Multiply (17 + X) * (-8 + X)
(17(-8 + X) + X(-8 + X)) = 21(X + -8)
((-8 * 17 + X * 17) + X(-8 + X)) = 21(X + -8)
((-136 + 17X) + X(-8 + X)) = 21(X + -8)
(-136 + 17X + (-8 * X + X * X)) = 21(X + -8)
(-136 + 17X + (-8X + X2)) = 21(X + -8)

Combine like terms: 17X + -8X = 9X
(-136 + 9X + X2) = 21(X + -8)

Reorder the terms:
-136 + 9X + X2 = 21(-8 + X)
-136 + 9X + X2 = (-8 * 21 + X * 21)
-136 + 9X + X2 = (-168 + 21X)

Solving
-136 + 9X + X2 = -168 + 21X

Solving for variable 'X'.

Reorder the terms:
-136 + 168 + 9X + -21X + X2 = -168 + 21X + 168 + -21X

Combine like terms: -136 + 168 = 32
32 + 9X + -21X + X2 = -168 + 21X + 168 + -21X

Combine like terms: 9X + -21X = -12X
32 + -12X + X2 = -168 + 21X + 168 + -21X

Reorder the terms:
32 + -12X + X2 = -168 + 168 + 21X + -21X

Combine like terms: -168 + 168 = 0
32 + -12X + X2 = 0 + 21X + -21X
32 + -12X + X2 = 21X + -21X

Combine like terms: 21X + -21X = 0
32 + -12X + X2 = 0

Factor a trinomial.
(4 + -1X)(8 + -1X) = 0


Subproblem 1
Set the factor '(4 + -1X)' equal to zero and attempt to solve:

Simplifying
4 + -1X = 0

Solving
4 + -1X = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1X = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1X = 0 + -4
-1X = 0 + -4

Combine like terms: 0 + -4 = -4
-1X = -4

Divide each side by '-1'.
X = 4

Simplifying
X = 4

Subproblem 2
Set the factor '(8 + -1X)' equal to zero and attempt to solve:

Simplifying
8 + -1X = 0

Solving
8 + -1X = 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 + -1X = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1X = 0 + -8
-1X = 0 + -8

Combine like terms: 0 + -8 = -8
-1X = -8

Divide each side by '-1'.
X = 8

Simplifying
X = 8
Solution
X = {4, 8}

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