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

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


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

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

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

Multiply (-3 + x) * (6 + x)
(-3(6 + x) + x(6 + x)) = 6x
((6 * -3 + x * -3) + x(6 + x)) = 6x
((-18 + -3x) + x(6 + x)) = 6x
(-18 + -3x + (6 * x + x * x)) = 6x
(-18 + -3x + (6x + x2)) = 6x

Combine like terms: -3x + 6x = 3x
(-18 + 3x + x2) = 6x

Solving
-18 + 3x + x2 = 6x

Solving for variable 'x'.

Reorder the terms:
-18 + 3x + -6x + x2 = 6x + -6x

Combine like terms: 3x + -6x = -3x
-18 + -3x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-18 + -3x + x2 = 0

Factor a trinomial.
(-3 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-3, 6}

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