(2x-1)(3x-5)=20

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Solution for (2x-1)(3x-5)=20 equation: 


Simplifying
(2x + -1)(3x + -5) = 20

Reorder the terms:
(-1 + 2x)(3x + -5) = 20

Reorder the terms:
(-1 + 2x)(-5 + 3x) = 20

Multiply (-1 + 2x) * (-5 + 3x)
(-1(-5 + 3x) + 2x * (-5 + 3x)) = 20
((-5 * -1 + 3x * -1) + 2x * (-5 + 3x)) = 20
((5 + -3x) + 2x * (-5 + 3x)) = 20
(5 + -3x + (-5 * 2x + 3x * 2x)) = 20
(5 + -3x + (-10x + 6x2)) = 20

Combine like terms: -3x + -10x = -13x
(5 + -13x + 6x2) = 20

Solving
5 + -13x + 6x2 = 20

Solving for variable 'x'.

Reorder the terms:
5 + -20 + -13x + 6x2 = 20 + -20

Combine like terms: 5 + -20 = -15
-15 + -13x + 6x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-15 + -13x + 6x2 = 0

Factor a trinomial.
(-5 + -6x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -6x)' equal to zero and attempt to solve:

Simplifying
-5 + -6x = 0

Solving
-5 + -6x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -6x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6x = 0 + 5
-6x = 0 + 5

Combine like terms: 0 + 5 = 5
-6x = 5

Divide each side by '-6'.
x = -0.8333333333

Simplifying
x = -0.8333333333

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.8333333333, 3}

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