3x(2x+4)=6(2x^2+1)

Solution for 3x(2x+4)=6(2x^2+1) equation:

Simplifying
3x(2x + 4) = 6(2x2 + 1)

Reorder the terms:
3x(4 + 2x) = 6(2x2 + 1)
(4 * 3x + 2x * 3x) = 6(2x2 + 1)
(12x + 6x2) = 6(2x2 + 1)

Reorder the terms:
12x + 6x2 = 6(1 + 2x2)
12x + 6x2 = (1 * 6 + 2x2 * 6)
12x + 6x2 = (6 + 12x2)

Solving
12x + 6x2 = 6 + 12x2

Solving for variable 'x'.

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

Combine like terms: 6x2 + -12x2 = -6x2
-6 + 12x + -6x2 = 6 + 12x2 + -6 + -12x2

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

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

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

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 2x + -1x2) = 0

Factor a trinomial.
6((-1 + x)(1 + -1x)) = 0

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

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {1, 1}