(x+9)(4x-5)=(x-17)(1-3x)

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Solution for (x+9)(4x-5)=(x-17)(1-3x) equation: 


Simplifying
(x + 9)(4x + -5) = (x + -17)(1 + -3x)

Reorder the terms:
(9 + x)(4x + -5) = (x + -17)(1 + -3x)

Reorder the terms:
(9 + x)(-5 + 4x) = (x + -17)(1 + -3x)

Multiply (9 + x) * (-5 + 4x)
(9(-5 + 4x) + x(-5 + 4x)) = (x + -17)(1 + -3x)
((-5 * 9 + 4x * 9) + x(-5 + 4x)) = (x + -17)(1 + -3x)
((-45 + 36x) + x(-5 + 4x)) = (x + -17)(1 + -3x)
(-45 + 36x + (-5 * x + 4x * x)) = (x + -17)(1 + -3x)
(-45 + 36x + (-5x + 4x2)) = (x + -17)(1 + -3x)

Combine like terms: 36x + -5x = 31x
(-45 + 31x + 4x2) = (x + -17)(1 + -3x)

Reorder the terms:
-45 + 31x + 4x2 = (-17 + x)(1 + -3x)

Multiply (-17 + x) * (1 + -3x)
-45 + 31x + 4x2 = (-17(1 + -3x) + x(1 + -3x))
-45 + 31x + 4x2 = ((1 * -17 + -3x * -17) + x(1 + -3x))
-45 + 31x + 4x2 = ((-17 + 51x) + x(1 + -3x))
-45 + 31x + 4x2 = (-17 + 51x + (1 * x + -3x * x))
-45 + 31x + 4x2 = (-17 + 51x + (1x + -3x2))

Combine like terms: 51x + 1x = 52x
-45 + 31x + 4x2 = (-17 + 52x + -3x2)

Solving
-45 + 31x + 4x2 = -17 + 52x + -3x2

Solving for variable 'x'.

Reorder the terms:
-45 + 17 + 31x + -52x + 4x2 + 3x2 = -17 + 52x + -3x2 + 17 + -52x + 3x2

Combine like terms: -45 + 17 = -28
-28 + 31x + -52x + 4x2 + 3x2 = -17 + 52x + -3x2 + 17 + -52x + 3x2

Combine like terms: 31x + -52x = -21x
-28 + -21x + 4x2 + 3x2 = -17 + 52x + -3x2 + 17 + -52x + 3x2

Combine like terms: 4x2 + 3x2 = 7x2
-28 + -21x + 7x2 = -17 + 52x + -3x2 + 17 + -52x + 3x2

Reorder the terms:
-28 + -21x + 7x2 = -17 + 17 + 52x + -52x + -3x2 + 3x2

Combine like terms: -17 + 17 = 0
-28 + -21x + 7x2 = 0 + 52x + -52x + -3x2 + 3x2
-28 + -21x + 7x2 = 52x + -52x + -3x2 + 3x2

Combine like terms: 52x + -52x = 0
-28 + -21x + 7x2 = 0 + -3x2 + 3x2
-28 + -21x + 7x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-28 + -21x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-4 + -3x + x2) = 0

Factor a trinomial.
7((-1 + -1x)(4 + -1x)) = 0

Ignore the factor 7.

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 '(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
Solution
x = {-1, 4}

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