(x+5)(5+3x)=1000

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Solution for (x+5)(5+3x)=1000 equation: 


Simplifying
(x + 5)(5 + 3x) = 1000

Reorder the terms:
(5 + x)(5 + 3x) = 1000

Multiply (5 + x) * (5 + 3x)
(5(5 + 3x) + x(5 + 3x)) = 1000
((5 * 5 + 3x * 5) + x(5 + 3x)) = 1000
((25 + 15x) + x(5 + 3x)) = 1000
(25 + 15x + (5 * x + 3x * x)) = 1000
(25 + 15x + (5x + 3x2)) = 1000

Combine like terms: 15x + 5x = 20x
(25 + 20x + 3x2) = 1000

Solving
25 + 20x + 3x2 = 1000

Solving for variable 'x'.

Reorder the terms:
25 + -1000 + 20x + 3x2 = 1000 + -1000

Combine like terms: 25 + -1000 = -975
-975 + 20x + 3x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-975 + 20x + 3x2 = 0

Factor a trinomial.
(-65 + -3x)(15 + -1x) = 0


Subproblem 1
Set the factor '(-65 + -3x)' equal to zero and attempt to solve:

Simplifying
-65 + -3x = 0

Solving
-65 + -3x = 0

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

Add '65' to each side of the equation.
-65 + 65 + -3x = 0 + 65

Combine like terms: -65 + 65 = 0
0 + -3x = 0 + 65
-3x = 0 + 65

Combine like terms: 0 + 65 = 65
-3x = 65

Divide each side by '-3'.
x = -21.66666667

Simplifying
x = -21.66666667

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 = {-21.66666667, 15}

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