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

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


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

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

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

Multiply (1 + 3x) * (-3 + 2x)
(1(-3 + 2x) + 3x * (-3 + 2x)) = (3x + 1)(5x + -3)
((-3 * 1 + 2x * 1) + 3x * (-3 + 2x)) = (3x + 1)(5x + -3)
((-3 + 2x) + 3x * (-3 + 2x)) = (3x + 1)(5x + -3)
(-3 + 2x + (-3 * 3x + 2x * 3x)) = (3x + 1)(5x + -3)
(-3 + 2x + (-9x + 6x2)) = (3x + 1)(5x + -3)

Combine like terms: 2x + -9x = -7x
(-3 + -7x + 6x2) = (3x + 1)(5x + -3)

Reorder the terms:
-3 + -7x + 6x2 = (1 + 3x)(5x + -3)

Reorder the terms:
-3 + -7x + 6x2 = (1 + 3x)(-3 + 5x)

Multiply (1 + 3x) * (-3 + 5x)
-3 + -7x + 6x2 = (1(-3 + 5x) + 3x * (-3 + 5x))
-3 + -7x + 6x2 = ((-3 * 1 + 5x * 1) + 3x * (-3 + 5x))
-3 + -7x + 6x2 = ((-3 + 5x) + 3x * (-3 + 5x))
-3 + -7x + 6x2 = (-3 + 5x + (-3 * 3x + 5x * 3x))
-3 + -7x + 6x2 = (-3 + 5x + (-9x + 15x2))

Combine like terms: 5x + -9x = -4x
-3 + -7x + 6x2 = (-3 + -4x + 15x2)

Add '3' to each side of the equation.
-3 + -7x + 3 + 6x2 = -3 + -4x + 3 + 15x2

Reorder the terms:
-3 + 3 + -7x + 6x2 = -3 + -4x + 3 + 15x2

Combine like terms: -3 + 3 = 0
0 + -7x + 6x2 = -3 + -4x + 3 + 15x2
-7x + 6x2 = -3 + -4x + 3 + 15x2

Reorder the terms:
-7x + 6x2 = -3 + 3 + -4x + 15x2

Combine like terms: -3 + 3 = 0
-7x + 6x2 = 0 + -4x + 15x2
-7x + 6x2 = -4x + 15x2

Solving
-7x + 6x2 = -4x + 15x2

Solving for variable 'x'.

Reorder the terms:
-7x + 4x + 6x2 + -15x2 = -4x + 15x2 + 4x + -15x2

Combine like terms: -7x + 4x = -3x
-3x + 6x2 + -15x2 = -4x + 15x2 + 4x + -15x2

Combine like terms: 6x2 + -15x2 = -9x2
-3x + -9x2 = -4x + 15x2 + 4x + -15x2

Reorder the terms:
-3x + -9x2 = -4x + 4x + 15x2 + -15x2

Combine like terms: -4x + 4x = 0
-3x + -9x2 = 0 + 15x2 + -15x2
-3x + -9x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-3x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-3x'.
-3x(1 + 3x) = 0

Ignore the factor -3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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, -0.3333333333}

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