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

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


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

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

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

Multiply (-1 + 2X) * (-2 + 3X)
(-1(-2 + 3X) + 2X * (-2 + 3X)) = 5X + 2
((-2 * -1 + 3X * -1) + 2X * (-2 + 3X)) = 5X + 2
((2 + -3X) + 2X * (-2 + 3X)) = 5X + 2
(2 + -3X + (-2 * 2X + 3X * 2X)) = 5X + 2
(2 + -3X + (-4X + 6X2)) = 5X + 2

Combine like terms: -3X + -4X = -7X
(2 + -7X + 6X2) = 5X + 2

Reorder the terms:
2 + -7X + 6X2 = 2 + 5X

Add '-2' to each side of the equation.
2 + -7X + -2 + 6X2 = 2 + -2 + 5X

Reorder the terms:
2 + -2 + -7X + 6X2 = 2 + -2 + 5X

Combine like terms: 2 + -2 = 0
0 + -7X + 6X2 = 2 + -2 + 5X
-7X + 6X2 = 2 + -2 + 5X

Combine like terms: 2 + -2 = 0
-7X + 6X2 = 0 + 5X
-7X + 6X2 = 5X

Solving
-7X + 6X2 = 5X

Solving for variable 'X'.

Reorder the terms:
-7X + -5X + 6X2 = 5X + -5X

Combine like terms: -7X + -5X = -12X
-12X + 6X2 = 5X + -5X

Combine like terms: 5X + -5X = 0
-12X + 6X2 = 0

Factor out the Greatest Common Factor (GCF), '6X'.
6X(-2 + X) = 0

Ignore the factor 6.

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 '(-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
Solution
X = {0, 2}

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