(X-5)(4X+3)=-9(X-5)

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Solution for (X-5)(4X+3)=-9(X-5) equation: 


Simplifying
(X + -5)(4X + 3) = -9(X + -5)

Reorder the terms:
(-5 + X)(4X + 3) = -9(X + -5)

Reorder the terms:
(-5 + X)(3 + 4X) = -9(X + -5)

Multiply (-5 + X) * (3 + 4X)
(-5(3 + 4X) + X(3 + 4X)) = -9(X + -5)
((3 * -5 + 4X * -5) + X(3 + 4X)) = -9(X + -5)
((-15 + -20X) + X(3 + 4X)) = -9(X + -5)
(-15 + -20X + (3 * X + 4X * X)) = -9(X + -5)
(-15 + -20X + (3X + 4X2)) = -9(X + -5)

Combine like terms: -20X + 3X = -17X
(-15 + -17X + 4X2) = -9(X + -5)

Reorder the terms:
-15 + -17X + 4X2 = -9(-5 + X)
-15 + -17X + 4X2 = (-5 * -9 + X * -9)
-15 + -17X + 4X2 = (45 + -9X)

Solving
-15 + -17X + 4X2 = 45 + -9X

Solving for variable 'X'.

Reorder the terms:
-15 + -45 + -17X + 9X + 4X2 = 45 + -9X + -45 + 9X

Combine like terms: -15 + -45 = -60
-60 + -17X + 9X + 4X2 = 45 + -9X + -45 + 9X

Combine like terms: -17X + 9X = -8X
-60 + -8X + 4X2 = 45 + -9X + -45 + 9X

Reorder the terms:
-60 + -8X + 4X2 = 45 + -45 + -9X + 9X

Combine like terms: 45 + -45 = 0
-60 + -8X + 4X2 = 0 + -9X + 9X
-60 + -8X + 4X2 = -9X + 9X

Combine like terms: -9X + 9X = 0
-60 + -8X + 4X2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -2X + X2) = 0

Factor a trinomial.
4((-3 + -1X)(5 + -1X)) = 0

Ignore the factor 4.

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 '(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
Solution
X = {-3, 5}

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