(3X-1)(2X-3)=10

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Solution for (3X-1)(2X-3)=10 equation: 


Simplifying
(3X + -1)(2X + -3) = 10

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

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

Multiply (-1 + 3X) * (-3 + 2X)
(-1(-3 + 2X) + 3X * (-3 + 2X)) = 10
((-3 * -1 + 2X * -1) + 3X * (-3 + 2X)) = 10
((3 + -2X) + 3X * (-3 + 2X)) = 10
(3 + -2X + (-3 * 3X + 2X * 3X)) = 10
(3 + -2X + (-9X + 6X2)) = 10

Combine like terms: -2X + -9X = -11X
(3 + -11X + 6X2) = 10

Solving
3 + -11X + 6X2 = 10

Solving for variable 'X'.

Reorder the terms:
3 + -10 + -11X + 6X2 = 10 + -10

Combine like terms: 3 + -10 = -7
-7 + -11X + 6X2 = 10 + -10

Combine like terms: 10 + -10 = 0
-7 + -11X + 6X2 = 0

Factor a trinomial.
(-1 + -2X)(7 + -3X) = 0


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

Simplifying
-1 + -2X = 0

Solving
-1 + -2X = 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 + -2X = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2X = 0 + 1
-2X = 0 + 1

Combine like terms: 0 + 1 = 1
-2X = 1

Divide each side by '-2'.
X = -0.5

Simplifying
X = -0.5

Subproblem 2
Set the factor '(7 + -3X)' equal to zero and attempt to solve:

Simplifying
7 + -3X = 0

Solving
7 + -3X = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3X = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3X = 0 + -7
-3X = 0 + -7

Combine like terms: 0 + -7 = -7
-3X = -7

Divide each side by '-3'.
X = 2.333333333

Simplifying
X = 2.333333333
Solution
X = {-0.5, 2.333333333}

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