(x-7)(x+9)=3(x-17)

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Solution for (x-7)(x+9)=3(x-17) equation: 


Simplifying
(x + -7)(x + 9) = 3(x + -17)

Reorder the terms:
(-7 + x)(x + 9) = 3(x + -17)

Reorder the terms:
(-7 + x)(9 + x) = 3(x + -17)

Multiply (-7 + x) * (9 + x)
(-7(9 + x) + x(9 + x)) = 3(x + -17)
((9 * -7 + x * -7) + x(9 + x)) = 3(x + -17)
((-63 + -7x) + x(9 + x)) = 3(x + -17)
(-63 + -7x + (9 * x + x * x)) = 3(x + -17)
(-63 + -7x + (9x + x2)) = 3(x + -17)

Combine like terms: -7x + 9x = 2x
(-63 + 2x + x2) = 3(x + -17)

Reorder the terms:
-63 + 2x + x2 = 3(-17 + x)
-63 + 2x + x2 = (-17 * 3 + x * 3)
-63 + 2x + x2 = (-51 + 3x)

Solving
-63 + 2x + x2 = -51 + 3x

Solving for variable 'x'.

Reorder the terms:
-63 + 51 + 2x + -3x + x2 = -51 + 3x + 51 + -3x

Combine like terms: -63 + 51 = -12
-12 + 2x + -3x + x2 = -51 + 3x + 51 + -3x

Combine like terms: 2x + -3x = -1x
-12 + -1x + x2 = -51 + 3x + 51 + -3x

Reorder the terms:
-12 + -1x + x2 = -51 + 51 + 3x + -3x

Combine like terms: -51 + 51 = 0
-12 + -1x + x2 = 0 + 3x + -3x
-12 + -1x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-12 + -1x + x2 = 0

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


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 '(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 = {-3, 4}

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