(2X-5)(X-5)=-3

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Solution for (2X-5)(X-5)=-3 equation: 


Simplifying
(2X + -5)(X + -5) = -3

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

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

Multiply (-5 + 2X) * (-5 + X)
(-5(-5 + X) + 2X * (-5 + X)) = -3
((-5 * -5 + X * -5) + 2X * (-5 + X)) = -3
((25 + -5X) + 2X * (-5 + X)) = -3
(25 + -5X + (-5 * 2X + X * 2X)) = -3
(25 + -5X + (-10X + 2X2)) = -3

Combine like terms: -5X + -10X = -15X
(25 + -15X + 2X2) = -3

Solving
25 + -15X + 2X2 = -3

Solving for variable 'X'.

Reorder the terms:
25 + 3 + -15X + 2X2 = -3 + 3

Combine like terms: 25 + 3 = 28
28 + -15X + 2X2 = -3 + 3

Combine like terms: -3 + 3 = 0
28 + -15X + 2X2 = 0

Factor a trinomial.
(7 + -2X)(4 + -1X) = 0


Subproblem 1
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

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 = {3.5, 4}

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