2x(3x-4)=2(3x*2+8)

Solution for 2x(3x-4)=2(3x*2+8) equation:

Simplifying
2x(3x + -4) = 2(3x * 2 + 8)

Reorder the terms:
2x(-4 + 3x) = 2(3x * 2 + 8)
(-4 * 2x + 3x * 2x) = 2(3x * 2 + 8)
(-8x + 6x2) = 2(3x * 2 + 8)

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

Multiply 3 * 2
-8x + 6x2 = 2(6x + 8)

Reorder the terms:
-8x + 6x2 = 2(8 + 6x)
-8x + 6x2 = (8 * 2 + 6x * 2)
-8x + 6x2 = (16 + 12x)

Solving
-8x + 6x2 = 16 + 12x

Solving for variable 'x'.

Reorder the terms:
-16 + -8x + -12x + 6x2 = 16 + 12x + -16 + -12x

Combine like terms: -8x + -12x = -20x
-16 + -20x + 6x2 = 16 + 12x + -16 + -12x

Reorder the terms:
-16 + -20x + 6x2 = 16 + -16 + 12x + -12x

Combine like terms: 16 + -16 = 0
-16 + -20x + 6x2 = 0 + 12x + -12x
-16 + -20x + 6x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-16 + -20x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -10x + 3x2) = 0

Factor a trinomial.
2((-2 + -3x)(4 + -1x)) = 0

Ignore the factor 2.
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 '(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
Solution
x = {-0.6666666667, 4}