(3x-1)(x+2)=(3x-1)(7x-10)

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Solution for (3x-1)(x+2)=(3x-1)(7x-10) equation: 


Simplifying
(3x + -1)(x + 2) = (3x + -1)(7x + -10)

Reorder the terms:
(-1 + 3x)(x + 2) = (3x + -1)(7x + -10)

Reorder the terms:
(-1 + 3x)(2 + x) = (3x + -1)(7x + -10)

Multiply (-1 + 3x) * (2 + x)
(-1(2 + x) + 3x * (2 + x)) = (3x + -1)(7x + -10)
((2 * -1 + x * -1) + 3x * (2 + x)) = (3x + -1)(7x + -10)
((-2 + -1x) + 3x * (2 + x)) = (3x + -1)(7x + -10)
(-2 + -1x + (2 * 3x + x * 3x)) = (3x + -1)(7x + -10)
(-2 + -1x + (6x + 3x2)) = (3x + -1)(7x + -10)

Combine like terms: -1x + 6x = 5x
(-2 + 5x + 3x2) = (3x + -1)(7x + -10)

Reorder the terms:
-2 + 5x + 3x2 = (-1 + 3x)(7x + -10)

Reorder the terms:
-2 + 5x + 3x2 = (-1 + 3x)(-10 + 7x)

Multiply (-1 + 3x) * (-10 + 7x)
-2 + 5x + 3x2 = (-1(-10 + 7x) + 3x * (-10 + 7x))
-2 + 5x + 3x2 = ((-10 * -1 + 7x * -1) + 3x * (-10 + 7x))
-2 + 5x + 3x2 = ((10 + -7x) + 3x * (-10 + 7x))
-2 + 5x + 3x2 = (10 + -7x + (-10 * 3x + 7x * 3x))
-2 + 5x + 3x2 = (10 + -7x + (-30x + 21x2))

Combine like terms: -7x + -30x = -37x
-2 + 5x + 3x2 = (10 + -37x + 21x2)

Solving
-2 + 5x + 3x2 = 10 + -37x + 21x2

Solving for variable 'x'.

Reorder the terms:
-2 + -10 + 5x + 37x + 3x2 + -21x2 = 10 + -37x + 21x2 + -10 + 37x + -21x2

Combine like terms: -2 + -10 = -12
-12 + 5x + 37x + 3x2 + -21x2 = 10 + -37x + 21x2 + -10 + 37x + -21x2

Combine like terms: 5x + 37x = 42x
-12 + 42x + 3x2 + -21x2 = 10 + -37x + 21x2 + -10 + 37x + -21x2

Combine like terms: 3x2 + -21x2 = -18x2
-12 + 42x + -18x2 = 10 + -37x + 21x2 + -10 + 37x + -21x2

Reorder the terms:
-12 + 42x + -18x2 = 10 + -10 + -37x + 37x + 21x2 + -21x2

Combine like terms: 10 + -10 = 0
-12 + 42x + -18x2 = 0 + -37x + 37x + 21x2 + -21x2
-12 + 42x + -18x2 = -37x + 37x + 21x2 + -21x2

Combine like terms: -37x + 37x = 0
-12 + 42x + -18x2 = 0 + 21x2 + -21x2
-12 + 42x + -18x2 = 21x2 + -21x2

Combine like terms: 21x2 + -21x2 = 0
-12 + 42x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + 7x + -3x2) = 0

Factor a trinomial.
6((-2 + x)(1 + -3x)) = 0

Ignore the factor 6.

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

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

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

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2

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 = {2, 0.3333333333}

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