0=(2x-5)(x-3)

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Solution for 0=(2x-5)(x-3) equation: 


Simplifying
0 = (2x + -5)(x + -3)

Reorder the terms:
0 = (-5 + 2x)(x + -3)

Reorder the terms:
0 = (-5 + 2x)(-3 + x)

Multiply (-5 + 2x) * (-3 + x)
0 = (-5(-3 + x) + 2x * (-3 + x))
0 = ((-3 * -5 + x * -5) + 2x * (-3 + x))
0 = ((15 + -5x) + 2x * (-3 + x))
0 = (15 + -5x + (-3 * 2x + x * 2x))
0 = (15 + -5x + (-6x + 2x2))

Combine like terms: -5x + -6x = -11x
0 = (15 + -11x + 2x2)

Solving
0 = 15 + -11x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + 11x + -2x2 = 15 + -11x + 2x2 + -15 + 11x + -2x2

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

Combine like terms: 15 + -15 = 0
-15 + 11x + -2x2 = 0 + -11x + 11x + 2x2 + -2x2
-15 + 11x + -2x2 = -11x + 11x + 2x2 + -2x2

Combine like terms: -11x + 11x = 0
-15 + 11x + -2x2 = 0 + 2x2 + -2x2
-15 + 11x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15 + 11x + -2x2 = 0

Factor a trinomial.
(-3 + x)(5 + -2x) = 0


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

Simplifying
-3 + x = 0

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

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

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

Simplifying
x = 3

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {3, 2.5}

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