(3x-1)(2x+1)+5x(3x-1)=0

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Solution for (3x-1)(2x+1)+5x(3x-1)=0 equation: 


Simplifying
(3x + -1)(2x + 1) + 5x(3x + -1) = 0

Reorder the terms:
(-1 + 3x)(2x + 1) + 5x(3x + -1) = 0

Reorder the terms:
(-1 + 3x)(1 + 2x) + 5x(3x + -1) = 0

Multiply (-1 + 3x) * (1 + 2x)
(-1(1 + 2x) + 3x * (1 + 2x)) + 5x(3x + -1) = 0
((1 * -1 + 2x * -1) + 3x * (1 + 2x)) + 5x(3x + -1) = 0
((-1 + -2x) + 3x * (1 + 2x)) + 5x(3x + -1) = 0
(-1 + -2x + (1 * 3x + 2x * 3x)) + 5x(3x + -1) = 0
(-1 + -2x + (3x + 6x2)) + 5x(3x + -1) = 0

Combine like terms: -2x + 3x = 1x
(-1 + 1x + 6x2) + 5x(3x + -1) = 0

Reorder the terms:
-1 + 1x + 6x2 + 5x(-1 + 3x) = 0
-1 + 1x + 6x2 + (-1 * 5x + 3x * 5x) = 0
-1 + 1x + 6x2 + (-5x + 15x2) = 0

Reorder the terms:
-1 + 1x + -5x + 6x2 + 15x2 = 0

Combine like terms: 1x + -5x = -4x
-1 + -4x + 6x2 + 15x2 = 0

Combine like terms: 6x2 + 15x2 = 21x2
-1 + -4x + 21x2 = 0

Solving
-1 + -4x + 21x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -7x)(1 + -3x) = 0


Subproblem 1
Set the factor '(-1 + -7x)' equal to zero and attempt to solve:

Simplifying
-1 + -7x = 0

Solving
-1 + -7x = 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 + -7x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7x = 0 + 1
-7x = 0 + 1

Combine like terms: 0 + 1 = 1
-7x = 1

Divide each side by '-7'.
x = -0.1428571429

Simplifying
x = -0.1428571429

Subproblem 2
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
Solution
x = {-0.1428571429, 0.3333333333}

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