(x+5)(10+x)=10(x+20)

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Solution for (x+5)(10+x)=10(x+20) equation: 


Simplifying
(x + 5)(10 + x) = 10(x + 20)

Reorder the terms:
(5 + x)(10 + x) = 10(x + 20)

Multiply (5 + x) * (10 + x)
(5(10 + x) + x(10 + x)) = 10(x + 20)
((10 * 5 + x * 5) + x(10 + x)) = 10(x + 20)
((50 + 5x) + x(10 + x)) = 10(x + 20)
(50 + 5x + (10 * x + x * x)) = 10(x + 20)
(50 + 5x + (10x + x2)) = 10(x + 20)

Combine like terms: 5x + 10x = 15x
(50 + 15x + x2) = 10(x + 20)

Reorder the terms:
50 + 15x + x2 = 10(20 + x)
50 + 15x + x2 = (20 * 10 + x * 10)
50 + 15x + x2 = (200 + 10x)

Solving
50 + 15x + x2 = 200 + 10x

Solving for variable 'x'.

Reorder the terms:
50 + -200 + 15x + -10x + x2 = 200 + 10x + -200 + -10x

Combine like terms: 50 + -200 = -150
-150 + 15x + -10x + x2 = 200 + 10x + -200 + -10x

Combine like terms: 15x + -10x = 5x
-150 + 5x + x2 = 200 + 10x + -200 + -10x

Reorder the terms:
-150 + 5x + x2 = 200 + -200 + 10x + -10x

Combine like terms: 200 + -200 = 0
-150 + 5x + x2 = 0 + 10x + -10x
-150 + 5x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-150 + 5x + x2 = 0

Factor a trinomial.
(-15 + -1x)(10 + -1x) = 0


Subproblem 1
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

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 = {-15, 10}

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