(3x-1)(4x-3)=2x(3x+3)

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


Simplifying
(3x + -1)(4x + -3) = 2x(3x + 3)

Reorder the terms:
(-1 + 3x)(4x + -3) = 2x(3x + 3)

Reorder the terms:
(-1 + 3x)(-3 + 4x) = 2x(3x + 3)

Multiply (-1 + 3x) * (-3 + 4x)
(-1(-3 + 4x) + 3x * (-3 + 4x)) = 2x(3x + 3)
((-3 * -1 + 4x * -1) + 3x * (-3 + 4x)) = 2x(3x + 3)
((3 + -4x) + 3x * (-3 + 4x)) = 2x(3x + 3)
(3 + -4x + (-3 * 3x + 4x * 3x)) = 2x(3x + 3)
(3 + -4x + (-9x + 12x2)) = 2x(3x + 3)

Combine like terms: -4x + -9x = -13x
(3 + -13x + 12x2) = 2x(3x + 3)

Reorder the terms:
3 + -13x + 12x2 = 2x(3 + 3x)
3 + -13x + 12x2 = (3 * 2x + 3x * 2x)
3 + -13x + 12x2 = (6x + 6x2)

Solving
3 + -13x + 12x2 = 6x + 6x2

Solving for variable 'x'.

Reorder the terms:
3 + -13x + -6x + 12x2 + -6x2 = 6x + 6x2 + -6x + -6x2

Combine like terms: -13x + -6x = -19x
3 + -19x + 12x2 + -6x2 = 6x + 6x2 + -6x + -6x2

Combine like terms: 12x2 + -6x2 = 6x2
3 + -19x + 6x2 = 6x + 6x2 + -6x + -6x2

Reorder the terms:
3 + -19x + 6x2 = 6x + -6x + 6x2 + -6x2

Combine like terms: 6x + -6x = 0
3 + -19x + 6x2 = 0 + 6x2 + -6x2
3 + -19x + 6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
3 + -19x + 6x2 = 0

Factor a trinomial.
(1 + -6x)(3 + -1x) = 0


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

Simplifying
1 + -6x = 0

Solving
1 + -6x = 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 + -6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6x = 0 + -1
-6x = 0 + -1

Combine like terms: 0 + -1 = -1
-6x = -1

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.1666666667, 3}

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