(3x+2)(x-5)=9x+6

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Solution for (3x+2)(x-5)=9x+6 equation: 


Simplifying
(3x + 2)(x + -5) = 9x + 6

Reorder the terms:
(2 + 3x)(x + -5) = 9x + 6

Reorder the terms:
(2 + 3x)(-5 + x) = 9x + 6

Multiply (2 + 3x) * (-5 + x)
(2(-5 + x) + 3x * (-5 + x)) = 9x + 6
((-5 * 2 + x * 2) + 3x * (-5 + x)) = 9x + 6
((-10 + 2x) + 3x * (-5 + x)) = 9x + 6
(-10 + 2x + (-5 * 3x + x * 3x)) = 9x + 6
(-10 + 2x + (-15x + 3x2)) = 9x + 6

Combine like terms: 2x + -15x = -13x
(-10 + -13x + 3x2) = 9x + 6

Reorder the terms:
-10 + -13x + 3x2 = 6 + 9x

Solving
-10 + -13x + 3x2 = 6 + 9x

Solving for variable 'x'.

Reorder the terms:
-10 + -6 + -13x + -9x + 3x2 = 6 + 9x + -6 + -9x

Combine like terms: -10 + -6 = -16
-16 + -13x + -9x + 3x2 = 6 + 9x + -6 + -9x

Combine like terms: -13x + -9x = -22x
-16 + -22x + 3x2 = 6 + 9x + -6 + -9x

Reorder the terms:
-16 + -22x + 3x2 = 6 + -6 + 9x + -9x

Combine like terms: 6 + -6 = 0
-16 + -22x + 3x2 = 0 + 9x + -9x
-16 + -22x + 3x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-16 + -22x + 3x2 = 0

Factor a trinomial.
(-2 + -3x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-0.6666666667, 8}

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