x(3x+2)=-2(3x-8)

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Solution for x(3x+2)=-2(3x-8) equation: 


Simplifying
x(3x + 2) = -2(3x + -8)

Reorder the terms:
x(2 + 3x) = -2(3x + -8)
(2 * x + 3x * x) = -2(3x + -8)
(2x + 3x2) = -2(3x + -8)

Reorder the terms:
2x + 3x2 = -2(-8 + 3x)
2x + 3x2 = (-8 * -2 + 3x * -2)
2x + 3x2 = (16 + -6x)

Solving
2x + 3x2 = 16 + -6x

Solving for variable 'x'.

Reorder the terms:
-16 + 2x + 6x + 3x2 = 16 + -6x + -16 + 6x

Combine like terms: 2x + 6x = 8x
-16 + 8x + 3x2 = 16 + -6x + -16 + 6x

Reorder the terms:
-16 + 8x + 3x2 = 16 + -16 + -6x + 6x

Combine like terms: 16 + -16 = 0
-16 + 8x + 3x2 = 0 + -6x + 6x
-16 + 8x + 3x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-16 + 8x + 3x2 = 0

Factor a trinomial.
(-4 + -1x)(4 + -3x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-4, 1.333333333}

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