(x-6)(x+7)=3(x-9)

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Solution for (x-6)(x+7)=3(x-9) equation: 


Simplifying
(x + -6)(x + 7) = 3(x + -9)

Reorder the terms:
(-6 + x)(x + 7) = 3(x + -9)

Reorder the terms:
(-6 + x)(7 + x) = 3(x + -9)

Multiply (-6 + x) * (7 + x)
(-6(7 + x) + x(7 + x)) = 3(x + -9)
((7 * -6 + x * -6) + x(7 + x)) = 3(x + -9)
((-42 + -6x) + x(7 + x)) = 3(x + -9)
(-42 + -6x + (7 * x + x * x)) = 3(x + -9)
(-42 + -6x + (7x + x2)) = 3(x + -9)

Combine like terms: -6x + 7x = 1x
(-42 + 1x + x2) = 3(x + -9)

Reorder the terms:
-42 + 1x + x2 = 3(-9 + x)
-42 + 1x + x2 = (-9 * 3 + x * 3)
-42 + 1x + x2 = (-27 + 3x)

Solving
-42 + 1x + x2 = -27 + 3x

Solving for variable 'x'.

Reorder the terms:
-42 + 27 + 1x + -3x + x2 = -27 + 3x + 27 + -3x

Combine like terms: -42 + 27 = -15
-15 + 1x + -3x + x2 = -27 + 3x + 27 + -3x

Combine like terms: 1x + -3x = -2x
-15 + -2x + x2 = -27 + 3x + 27 + -3x

Reorder the terms:
-15 + -2x + x2 = -27 + 27 + 3x + -3x

Combine like terms: -27 + 27 = 0
-15 + -2x + x2 = 0 + 3x + -3x
-15 + -2x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-15 + -2x + x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -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 '(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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