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

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


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

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

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

Multiply (-1 + 2x) * (-2 + 3x)
(-1(-2 + 3x) + 2x * (-2 + 3x)) = 5
((-2 * -1 + 3x * -1) + 2x * (-2 + 3x)) = 5
((2 + -3x) + 2x * (-2 + 3x)) = 5
(2 + -3x + (-2 * 2x + 3x * 2x)) = 5
(2 + -3x + (-4x + 6x2)) = 5

Combine like terms: -3x + -4x = -7x
(2 + -7x + 6x2) = 5

Solving
2 + -7x + 6x2 = 5

Solving for variable 'x'.

Reorder the terms:
2 + -5 + -7x + 6x2 = 5 + -5

Combine like terms: 2 + -5 = -3
-3 + -7x + 6x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-3 + -7x + 6x2 = 0

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


Subproblem 1
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

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-0.3333333333, 1.5}

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