(2x-3)(x-1)=15

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Solution for (2x-3)(x-1)=15 equation: 


Simplifying
(2x + -3)(x + -1) = 15

Reorder the terms:
(-3 + 2x)(x + -1) = 15

Reorder the terms:
(-3 + 2x)(-1 + x) = 15

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

Combine like terms: -3x + -2x = -5x
(3 + -5x + 2x2) = 15

Solving
3 + -5x + 2x2 = 15

Solving for variable 'x'.

Reorder the terms:
3 + -15 + -5x + 2x2 = 15 + -15

Combine like terms: 3 + -15 = -12
-12 + -5x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-12 + -5x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(4 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1.5, 4}

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