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

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


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

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

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

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

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

Reorder the terms:
-2 + -5x + 3x2 = (-2 + x)(3x + 5)

Reorder the terms:
-2 + -5x + 3x2 = (-2 + x)(5 + 3x)

Multiply (-2 + x) * (5 + 3x)
-2 + -5x + 3x2 = (-2(5 + 3x) + x(5 + 3x))
-2 + -5x + 3x2 = ((5 * -2 + 3x * -2) + x(5 + 3x))
-2 + -5x + 3x2 = ((-10 + -6x) + x(5 + 3x))
-2 + -5x + 3x2 = (-10 + -6x + (5 * x + 3x * x))
-2 + -5x + 3x2 = (-10 + -6x + (5x + 3x2))

Combine like terms: -6x + 5x = -1x
-2 + -5x + 3x2 = (-10 + -1x + 3x2)

Add '-3x2' to each side of the equation.
-2 + -5x + 3x2 + -3x2 = -10 + -1x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-2 + -5x + 0 = -10 + -1x + 3x2 + -3x2
-2 + -5x = -10 + -1x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-2 + -5x = -10 + -1x + 0
-2 + -5x = -10 + -1x

Solving
-2 + -5x = -10 + -1x

Solving for variable 'x'.

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

Add 'x' to each side of the equation.
-2 + -5x + x = -10 + -1x + x

Combine like terms: -5x + x = -4x
-2 + -4x = -10 + -1x + x

Combine like terms: -1x + x = 0
-2 + -4x = -10 + 0
-2 + -4x = -10

Add '2' to each side of the equation.
-2 + 2 + -4x = -10 + 2

Combine like terms: -2 + 2 = 0
0 + -4x = -10 + 2
-4x = -10 + 2

Combine like terms: -10 + 2 = -8
-4x = -8

Divide each side by '-4'.
x = 2

Simplifying
x = 2

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