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

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


Simplifying
x2 + (x + 5)(x + 5) = (x + 10)(x + 10)

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

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

Multiply (5 + x) * (5 + x)
x2 + (5(5 + x) + x(5 + x)) = (x + 10)(x + 10)
x2 + ((5 * 5 + x * 5) + x(5 + x)) = (x + 10)(x + 10)
x2 + ((25 + 5x) + x(5 + x)) = (x + 10)(x + 10)
x2 + (25 + 5x + (5 * x + x * x)) = (x + 10)(x + 10)
x2 + (25 + 5x + (5x + x2)) = (x + 10)(x + 10)

Combine like terms: 5x + 5x = 10x
x2 + (25 + 10x + x2) = (x + 10)(x + 10)

Reorder the terms:
25 + 10x + x2 + x2 = (x + 10)(x + 10)

Combine like terms: x2 + x2 = 2x2
25 + 10x + 2x2 = (x + 10)(x + 10)

Reorder the terms:
25 + 10x + 2x2 = (10 + x)(x + 10)

Reorder the terms:
25 + 10x + 2x2 = (10 + x)(10 + x)

Multiply (10 + x) * (10 + x)
25 + 10x + 2x2 = (10(10 + x) + x(10 + x))
25 + 10x + 2x2 = ((10 * 10 + x * 10) + x(10 + x))
25 + 10x + 2x2 = ((100 + 10x) + x(10 + x))
25 + 10x + 2x2 = (100 + 10x + (10 * x + x * x))
25 + 10x + 2x2 = (100 + 10x + (10x + x2))

Combine like terms: 10x + 10x = 20x
25 + 10x + 2x2 = (100 + 20x + x2)

Solving
25 + 10x + 2x2 = 100 + 20x + x2

Solving for variable 'x'.

Reorder the terms:
25 + -100 + 10x + -20x + 2x2 + -1x2 = 100 + 20x + x2 + -100 + -20x + -1x2

Combine like terms: 25 + -100 = -75
-75 + 10x + -20x + 2x2 + -1x2 = 100 + 20x + x2 + -100 + -20x + -1x2

Combine like terms: 10x + -20x = -10x
-75 + -10x + 2x2 + -1x2 = 100 + 20x + x2 + -100 + -20x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-75 + -10x + 1x2 = 100 + 20x + x2 + -100 + -20x + -1x2

Reorder the terms:
-75 + -10x + 1x2 = 100 + -100 + 20x + -20x + x2 + -1x2

Combine like terms: 100 + -100 = 0
-75 + -10x + 1x2 = 0 + 20x + -20x + x2 + -1x2
-75 + -10x + 1x2 = 20x + -20x + x2 + -1x2

Combine like terms: 20x + -20x = 0
-75 + -10x + 1x2 = 0 + x2 + -1x2
-75 + -10x + 1x2 = x2 + -1x2

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

Factor a trinomial.
(-5 + -1x)(15 + -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 '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-5, 15}

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