(x-10)(2x-10)=600

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Solution for (x-10)(2x-10)=600 equation: 


Simplifying
(x + -10)(2x + -10) = 600

Reorder the terms:
(-10 + x)(2x + -10) = 600

Reorder the terms:
(-10 + x)(-10 + 2x) = 600

Multiply (-10 + x) * (-10 + 2x)
(-10(-10 + 2x) + x(-10 + 2x)) = 600
((-10 * -10 + 2x * -10) + x(-10 + 2x)) = 600
((100 + -20x) + x(-10 + 2x)) = 600
(100 + -20x + (-10 * x + 2x * x)) = 600
(100 + -20x + (-10x + 2x2)) = 600

Combine like terms: -20x + -10x = -30x
(100 + -30x + 2x2) = 600

Solving
100 + -30x + 2x2 = 600

Solving for variable 'x'.

Reorder the terms:
100 + -600 + -30x + 2x2 = 600 + -600

Combine like terms: 100 + -600 = -500
-500 + -30x + 2x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-500 + -30x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-250 + -15x + x2) = 0

Factor a trinomial.
2((-10 + -1x)(25 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(25 + -1x)' equal to zero and attempt to solve:

Simplifying
25 + -1x = 0

Solving
25 + -1x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1x = 0 + -25
-1x = 0 + -25

Combine like terms: 0 + -25 = -25
-1x = -25

Divide each side by '-1'.
x = 25

Simplifying
x = 25
Solution
x = {-10, 25}

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