2(3x-1)(3x-1)+13(3x-1)+21=0

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Solution for 2(3x-1)(3x-1)+13(3x-1)+21=0 equation: 


Simplifying
2(3x + -1)(3x + -1) + 13(3x + -1) + 21 = 0

Reorder the terms:
2(-1 + 3x)(3x + -1) + 13(3x + -1) + 21 = 0

Reorder the terms:
2(-1 + 3x)(-1 + 3x) + 13(3x + -1) + 21 = 0

Multiply (-1 + 3x) * (-1 + 3x)
2(-1(-1 + 3x) + 3x * (-1 + 3x)) + 13(3x + -1) + 21 = 0
2((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) + 13(3x + -1) + 21 = 0
2((1 + -3x) + 3x * (-1 + 3x)) + 13(3x + -1) + 21 = 0
2(1 + -3x + (-1 * 3x + 3x * 3x)) + 13(3x + -1) + 21 = 0
2(1 + -3x + (-3x + 9x2)) + 13(3x + -1) + 21 = 0

Combine like terms: -3x + -3x = -6x
2(1 + -6x + 9x2) + 13(3x + -1) + 21 = 0
(1 * 2 + -6x * 2 + 9x2 * 2) + 13(3x + -1) + 21 = 0
(2 + -12x + 18x2) + 13(3x + -1) + 21 = 0

Reorder the terms:
2 + -12x + 18x2 + 13(-1 + 3x) + 21 = 0
2 + -12x + 18x2 + (-1 * 13 + 3x * 13) + 21 = 0
2 + -12x + 18x2 + (-13 + 39x) + 21 = 0

Reorder the terms:
2 + -13 + 21 + -12x + 39x + 18x2 = 0

Combine like terms: 2 + -13 = -11
-11 + 21 + -12x + 39x + 18x2 = 0

Combine like terms: -11 + 21 = 10
10 + -12x + 39x + 18x2 = 0

Combine like terms: -12x + 39x = 27x
10 + 27x + 18x2 = 0

Solving
10 + 27x + 18x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + 6x)(2 + 3x) = 0


Subproblem 1
Set the factor '(5 + 6x)' equal to zero and attempt to solve:

Simplifying
5 + 6x = 0

Solving
5 + 6x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x = 0 + -5
6x = 0 + -5

Combine like terms: 0 + -5 = -5
6x = -5

Divide each side by '6'.
x = -0.8333333333

Simplifying
x = -0.8333333333

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 = {-0.8333333333, -0.6666666667}

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