(x-5)(2x-5)-75=0

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Solution for (x-5)(2x-5)-75=0 equation: 


Simplifying
(x + -5)(2x + -5) + -75 = 0

Reorder the terms:
(-5 + x)(2x + -5) + -75 = 0

Reorder the terms:
(-5 + x)(-5 + 2x) + -75 = 0

Multiply (-5 + x) * (-5 + 2x)
(-5(-5 + 2x) + x(-5 + 2x)) + -75 = 0
((-5 * -5 + 2x * -5) + x(-5 + 2x)) + -75 = 0
((25 + -10x) + x(-5 + 2x)) + -75 = 0
(25 + -10x + (-5 * x + 2x * x)) + -75 = 0
(25 + -10x + (-5x + 2x2)) + -75 = 0

Combine like terms: -10x + -5x = -15x
(25 + -15x + 2x2) + -75 = 0

Reorder the terms:
25 + -75 + -15x + 2x2 = 0

Combine like terms: 25 + -75 = -50
-50 + -15x + 2x2 = 0

Solving
-50 + -15x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -2x)(10 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-2.5, 10}

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