(3x+7)(6x-1)=27

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Solution for (3x+7)(6x-1)=27 equation: 


Simplifying
(3x + 7)(6x + -1) = 27

Reorder the terms:
(7 + 3x)(6x + -1) = 27

Reorder the terms:
(7 + 3x)(-1 + 6x) = 27

Multiply (7 + 3x) * (-1 + 6x)
(7(-1 + 6x) + 3x * (-1 + 6x)) = 27
((-1 * 7 + 6x * 7) + 3x * (-1 + 6x)) = 27
((-7 + 42x) + 3x * (-1 + 6x)) = 27
(-7 + 42x + (-1 * 3x + 6x * 3x)) = 27
(-7 + 42x + (-3x + 18x2)) = 27

Combine like terms: 42x + -3x = 39x
(-7 + 39x + 18x2) = 27

Solving
-7 + 39x + 18x2 = 27

Solving for variable 'x'.

Reorder the terms:
-7 + -27 + 39x + 18x2 = 27 + -27

Combine like terms: -7 + -27 = -34
-34 + 39x + 18x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-34 + 39x + 18x2 = 0

Factor a trinomial.
(-17 + -6x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-17 + -6x)' equal to zero and attempt to solve:

Simplifying
-17 + -6x = 0

Solving
-17 + -6x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -6x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -6x = 0 + 17
-6x = 0 + 17

Combine like terms: 0 + 17 = 17
-6x = 17

Divide each side by '-6'.
x = -2.833333333

Simplifying
x = -2.833333333

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-2.833333333, 0.6666666667}

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