(5x+2)(3x-1)=(3x-1)(6x-2)

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Solution for (5x+2)(3x-1)=(3x-1)(6x-2) equation: 


Simplifying
(5x + 2)(3x + -1) = (3x + -1)(6x + -2)

Reorder the terms:
(2 + 5x)(3x + -1) = (3x + -1)(6x + -2)

Reorder the terms:
(2 + 5x)(-1 + 3x) = (3x + -1)(6x + -2)

Multiply (2 + 5x) * (-1 + 3x)
(2(-1 + 3x) + 5x * (-1 + 3x)) = (3x + -1)(6x + -2)
((-1 * 2 + 3x * 2) + 5x * (-1 + 3x)) = (3x + -1)(6x + -2)
((-2 + 6x) + 5x * (-1 + 3x)) = (3x + -1)(6x + -2)
(-2 + 6x + (-1 * 5x + 3x * 5x)) = (3x + -1)(6x + -2)
(-2 + 6x + (-5x + 15x2)) = (3x + -1)(6x + -2)

Combine like terms: 6x + -5x = 1x
(-2 + 1x + 15x2) = (3x + -1)(6x + -2)

Reorder the terms:
-2 + 1x + 15x2 = (-1 + 3x)(6x + -2)

Reorder the terms:
-2 + 1x + 15x2 = (-1 + 3x)(-2 + 6x)

Multiply (-1 + 3x) * (-2 + 6x)
-2 + 1x + 15x2 = (-1(-2 + 6x) + 3x * (-2 + 6x))
-2 + 1x + 15x2 = ((-2 * -1 + 6x * -1) + 3x * (-2 + 6x))
-2 + 1x + 15x2 = ((2 + -6x) + 3x * (-2 + 6x))
-2 + 1x + 15x2 = (2 + -6x + (-2 * 3x + 6x * 3x))
-2 + 1x + 15x2 = (2 + -6x + (-6x + 18x2))

Combine like terms: -6x + -6x = -12x
-2 + 1x + 15x2 = (2 + -12x + 18x2)

Solving
-2 + 1x + 15x2 = 2 + -12x + 18x2

Solving for variable 'x'.

Reorder the terms:
-2 + -2 + 1x + 12x + 15x2 + -18x2 = 2 + -12x + 18x2 + -2 + 12x + -18x2

Combine like terms: -2 + -2 = -4
-4 + 1x + 12x + 15x2 + -18x2 = 2 + -12x + 18x2 + -2 + 12x + -18x2

Combine like terms: 1x + 12x = 13x
-4 + 13x + 15x2 + -18x2 = 2 + -12x + 18x2 + -2 + 12x + -18x2

Combine like terms: 15x2 + -18x2 = -3x2
-4 + 13x + -3x2 = 2 + -12x + 18x2 + -2 + 12x + -18x2

Reorder the terms:
-4 + 13x + -3x2 = 2 + -2 + -12x + 12x + 18x2 + -18x2

Combine like terms: 2 + -2 = 0
-4 + 13x + -3x2 = 0 + -12x + 12x + 18x2 + -18x2
-4 + 13x + -3x2 = -12x + 12x + 18x2 + -18x2

Combine like terms: -12x + 12x = 0
-4 + 13x + -3x2 = 0 + 18x2 + -18x2
-4 + 13x + -3x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
-4 + 13x + -3x2 = 0

Factor a trinomial.
(-4 + x)(1 + -3x) = 0


Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

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 = {4, 0.3333333333}

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