440=5*(5+x)*(5+2x)

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Solution for 440=5*(5+x)*(5+2x) equation: 


Simplifying
440 = 5(5 + x)(5 + 2x)

Multiply (5 + x) * (5 + 2x)
440 = 5(5(5 + 2x) + x(5 + 2x))
440 = 5((5 * 5 + 2x * 5) + x(5 + 2x))
440 = 5((25 + 10x) + x(5 + 2x))
440 = 5(25 + 10x + (5 * x + 2x * x))
440 = 5(25 + 10x + (5x + 2x2))

Combine like terms: 10x + 5x = 15x
440 = 5(25 + 15x + 2x2)
440 = (25 * 5 + 15x * 5 + 2x2 * 5)
440 = (125 + 75x + 10x2)

Solving
440 = 125 + 75x + 10x2

Solving for variable 'x'.

Combine like terms: 440 + -125 = 315
315 + -75x + -10x2 = 125 + 75x + 10x2 + -125 + -75x + -10x2

Reorder the terms:
315 + -75x + -10x2 = 125 + -125 + 75x + -75x + 10x2 + -10x2

Combine like terms: 125 + -125 = 0
315 + -75x + -10x2 = 0 + 75x + -75x + 10x2 + -10x2
315 + -75x + -10x2 = 75x + -75x + 10x2 + -10x2

Combine like terms: 75x + -75x = 0
315 + -75x + -10x2 = 0 + 10x2 + -10x2
315 + -75x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
315 + -75x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(63 + -15x + -2x2) = 0

Factor a trinomial.
5((3 + -1x)(21 + 2x)) = 0

Ignore the factor 5.

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(21 + 2x)' equal to zero and attempt to solve:

Simplifying
21 + 2x = 0

Solving
21 + 2x = 0

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

Add '-21' to each side of the equation.
21 + -21 + 2x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 2x = 0 + -21
2x = 0 + -21

Combine like terms: 0 + -21 = -21
2x = -21

Divide each side by '2'.
x = -10.5

Simplifying
x = -10.5
Solution
x = {3, -10.5}

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