(3x+2)(x-7)=6x+4

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Solution for (3x+2)(x-7)=6x+4 equation: 


Simplifying
(3x + 2)(x + -7) = 6x + 4

Reorder the terms:
(2 + 3x)(x + -7) = 6x + 4

Reorder the terms:
(2 + 3x)(-7 + x) = 6x + 4

Multiply (2 + 3x) * (-7 + x)
(2(-7 + x) + 3x * (-7 + x)) = 6x + 4
((-7 * 2 + x * 2) + 3x * (-7 + x)) = 6x + 4
((-14 + 2x) + 3x * (-7 + x)) = 6x + 4
(-14 + 2x + (-7 * 3x + x * 3x)) = 6x + 4
(-14 + 2x + (-21x + 3x2)) = 6x + 4

Combine like terms: 2x + -21x = -19x
(-14 + -19x + 3x2) = 6x + 4

Reorder the terms:
-14 + -19x + 3x2 = 4 + 6x

Solving
-14 + -19x + 3x2 = 4 + 6x

Solving for variable 'x'.

Reorder the terms:
-14 + -4 + -19x + -6x + 3x2 = 4 + 6x + -4 + -6x

Combine like terms: -14 + -4 = -18
-18 + -19x + -6x + 3x2 = 4 + 6x + -4 + -6x

Combine like terms: -19x + -6x = -25x
-18 + -25x + 3x2 = 4 + 6x + -4 + -6x

Reorder the terms:
-18 + -25x + 3x2 = 4 + -4 + 6x + -6x

Combine like terms: 4 + -4 = 0
-18 + -25x + 3x2 = 0 + 6x + -6x
-18 + -25x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-18 + -25x + 3x2 = 0

Factor a trinomial.
(-2 + -3x)(9 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-0.6666666667, 9}

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