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

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


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

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

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

Multiply (-3 + x) * (-5 + 2x)
(-3(-5 + 2x) + x(-5 + 2x)) = 1
((-5 * -3 + 2x * -3) + x(-5 + 2x)) = 1
((15 + -6x) + x(-5 + 2x)) = 1
(15 + -6x + (-5 * x + 2x * x)) = 1
(15 + -6x + (-5x + 2x2)) = 1

Combine like terms: -6x + -5x = -11x
(15 + -11x + 2x2) = 1

Solving
15 + -11x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
15 + -1 + -11x + 2x2 = 1 + -1

Combine like terms: 15 + -1 = 14
14 + -11x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
14 + -11x + 2x2 = 0

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


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {2, 3.5}

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