(3x-18+7)(x-6+4)=0

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Solution for (3x-18+7)(x-6+4)=0 equation: 


Simplifying
(3x + -18 + 7)(x + -6 + 4) = 0

Reorder the terms:
(-18 + 7 + 3x)(x + -6 + 4) = 0

Combine like terms: -18 + 7 = -11
(-11 + 3x)(x + -6 + 4) = 0

Reorder the terms:
(-11 + 3x)(-6 + 4 + x) = 0

Combine like terms: -6 + 4 = -2
(-11 + 3x)(-2 + x) = 0

Multiply (-11 + 3x) * (-2 + x)
(-11(-2 + x) + 3x * (-2 + x)) = 0
((-2 * -11 + x * -11) + 3x * (-2 + x)) = 0
((22 + -11x) + 3x * (-2 + x)) = 0
(22 + -11x + (-2 * 3x + x * 3x)) = 0
(22 + -11x + (-6x + 3x2)) = 0

Combine like terms: -11x + -6x = -17x
(22 + -17x + 3x2) = 0

Solving
22 + -17x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(11 + -3x) = 0


Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(11 + -3x)' equal to zero and attempt to solve:

Simplifying
11 + -3x = 0

Solving
11 + -3x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3x = 0 + -11
-3x = 0 + -11

Combine like terms: 0 + -11 = -11
-3x = -11

Divide each side by '-3'.
x = 3.666666667

Simplifying
x = 3.666666667
Solution
x = {2, 3.666666667}

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