(3x^2+2)(2)+(2x-3)(6x)=

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


Simplifying
(3x2 + 2)(2) + (2x + -3)(6x) = 0

Reorder the terms:
(2 + 3x2)(2) + (2x + -3)(6x) = 0

Reorder the terms for easier multiplication:
2(2 + 3x2) + (2x + -3)(6x) = 0
(2 * 2 + 3x2 * 2) + (2x + -3)(6x) = 0
(4 + 6x2) + (2x + -3)(6x) = 0

Reorder the terms:
4 + 6x2 + (-3 + 2x)(6x) = 0

Remove parenthesis around (6x)
4 + 6x2 + (-3 + 2x) * 6x = 0

Reorder the terms for easier multiplication:
4 + 6x2 + 6x(-3 + 2x) = 0
4 + 6x2 + (-3 * 6x + 2x * 6x) = 0
4 + 6x2 + (-18x + 12x2) = 0

Reorder the terms:
4 + -18x + 6x2 + 12x2 = 0

Combine like terms: 6x2 + 12x2 = 18x2
4 + -18x + 18x2 = 0

Solving
4 + -18x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -9x + 9x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 2
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
Solution
x = {0.3333333333, 0.6666666667}

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