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

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


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

Reorder the terms:
x(-9 + x) + 17 = 3(4 + -1x)
(-9 * x + x * x) + 17 = 3(4 + -1x)
(-9x + x2) + 17 = 3(4 + -1x)

Reorder the terms:
17 + -9x + x2 = 3(4 + -1x)
17 + -9x + x2 = (4 * 3 + -1x * 3)
17 + -9x + x2 = (12 + -3x)

Solving
17 + -9x + x2 = 12 + -3x

Solving for variable 'x'.

Reorder the terms:
17 + -12 + -9x + 3x + x2 = 12 + -3x + -12 + 3x

Combine like terms: 17 + -12 = 5
5 + -9x + 3x + x2 = 12 + -3x + -12 + 3x

Combine like terms: -9x + 3x = -6x
5 + -6x + x2 = 12 + -3x + -12 + 3x

Reorder the terms:
5 + -6x + x2 = 12 + -12 + -3x + 3x

Combine like terms: 12 + -12 = 0
5 + -6x + x2 = 0 + -3x + 3x
5 + -6x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
5 + -6x + x2 = 0

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


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 '(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 = {1, 5}

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