(2x-10)(x+5)=x^2+10x-75

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Solution for (2x-10)(x+5)=x^2+10x-75 equation: 


Simplifying
(2x + -10)(x + 5) = x2 + 10x + -75

Reorder the terms:
(-10 + 2x)(x + 5) = x2 + 10x + -75

Reorder the terms:
(-10 + 2x)(5 + x) = x2 + 10x + -75

Multiply (-10 + 2x) * (5 + x)
(-10(5 + x) + 2x * (5 + x)) = x2 + 10x + -75
((5 * -10 + x * -10) + 2x * (5 + x)) = x2 + 10x + -75
((-50 + -10x) + 2x * (5 + x)) = x2 + 10x + -75
(-50 + -10x + (5 * 2x + x * 2x)) = x2 + 10x + -75
(-50 + -10x + (10x + 2x2)) = x2 + 10x + -75

Combine like terms: -10x + 10x = 0
(-50 + 0 + 2x2) = x2 + 10x + -75
(-50 + 2x2) = x2 + 10x + -75

Reorder the terms:
-50 + 2x2 = -75 + 10x + x2

Solving
-50 + 2x2 = -75 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
-50 + 75 + -10x + 2x2 + -1x2 = -75 + 10x + x2 + 75 + -10x + -1x2

Combine like terms: -50 + 75 = 25
25 + -10x + 2x2 + -1x2 = -75 + 10x + x2 + 75 + -10x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
25 + -10x + 1x2 = -75 + 10x + x2 + 75 + -10x + -1x2

Reorder the terms:
25 + -10x + 1x2 = -75 + 75 + 10x + -10x + x2 + -1x2

Combine like terms: -75 + 75 = 0
25 + -10x + 1x2 = 0 + 10x + -10x + x2 + -1x2
25 + -10x + 1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
25 + -10x + 1x2 = 0 + x2 + -1x2
25 + -10x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
25 + -10x + 1x2 = 0

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


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {5, 5}

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