(X-9)(2X+1)=-5(X-9)

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Solution for (X-9)(2X+1)=-5(X-9) equation: 


Simplifying
(X + -9)(2X + 1) = -5(X + -9)

Reorder the terms:
(-9 + X)(2X + 1) = -5(X + -9)

Reorder the terms:
(-9 + X)(1 + 2X) = -5(X + -9)

Multiply (-9 + X) * (1 + 2X)
(-9(1 + 2X) + X(1 + 2X)) = -5(X + -9)
((1 * -9 + 2X * -9) + X(1 + 2X)) = -5(X + -9)
((-9 + -18X) + X(1 + 2X)) = -5(X + -9)
(-9 + -18X + (1 * X + 2X * X)) = -5(X + -9)
(-9 + -18X + (1X + 2X2)) = -5(X + -9)

Combine like terms: -18X + 1X = -17X
(-9 + -17X + 2X2) = -5(X + -9)

Reorder the terms:
-9 + -17X + 2X2 = -5(-9 + X)
-9 + -17X + 2X2 = (-9 * -5 + X * -5)
-9 + -17X + 2X2 = (45 + -5X)

Solving
-9 + -17X + 2X2 = 45 + -5X

Solving for variable 'X'.

Reorder the terms:
-9 + -45 + -17X + 5X + 2X2 = 45 + -5X + -45 + 5X

Combine like terms: -9 + -45 = -54
-54 + -17X + 5X + 2X2 = 45 + -5X + -45 + 5X

Combine like terms: -17X + 5X = -12X
-54 + -12X + 2X2 = 45 + -5X + -45 + 5X

Reorder the terms:
-54 + -12X + 2X2 = 45 + -45 + -5X + 5X

Combine like terms: 45 + -45 = 0
-54 + -12X + 2X2 = 0 + -5X + 5X
-54 + -12X + 2X2 = -5X + 5X

Combine like terms: -5X + 5X = 0
-54 + -12X + 2X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -6X + X2) = 0

Factor a trinomial.
2((-3 + -1X)(9 + -1X)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -1X)' equal to zero and attempt to solve:

Simplifying
-3 + -1X = 0

Solving
-3 + -1X = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1X = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1X = 0 + 3
-1X = 0 + 3

Combine like terms: 0 + 3 = 3
-1X = 3

Divide each side by '-1'.
X = -3

Simplifying
X = -3

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 = {-3, 9}

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