(2x-3)(x-1)=36

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Solution for (2x-3)(x-1)=36 equation: 


Simplifying
(2x + -3)(x + -1) = 36

Reorder the terms:
(-3 + 2x)(x + -1) = 36

Reorder the terms:
(-3 + 2x)(-1 + x) = 36

Multiply (-3 + 2x) * (-1 + x)
(-3(-1 + x) + 2x * (-1 + x)) = 36
((-1 * -3 + x * -3) + 2x * (-1 + x)) = 36
((3 + -3x) + 2x * (-1 + x)) = 36
(3 + -3x + (-1 * 2x + x * 2x)) = 36
(3 + -3x + (-2x + 2x2)) = 36

Combine like terms: -3x + -2x = -5x
(3 + -5x + 2x2) = 36

Solving
3 + -5x + 2x2 = 36

Solving for variable 'x'.

Reorder the terms:
3 + -36 + -5x + 2x2 = 36 + -36

Combine like terms: 3 + -36 = -33
-33 + -5x + 2x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-33 + -5x + 2x2 = 0

Factor a trinomial.
(-3 + -1x)(11 + -2x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {-3, 5.5}

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