90=(x+2)(5x)

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Solution for 90=(x+2)(5x) equation: 


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

Reorder the terms:
90 = (2 + x)(5x)

Remove parenthesis around (5x)
90 = (2 + x) * 5x

Reorder the terms for easier multiplication:
90 = 5x(2 + x)
90 = (2 * 5x + x * 5x)
90 = (10x + 5x2)

Solving
90 = 10x + 5x2

Solving for variable 'x'.

Reorder the terms:
90 + -10x + -5x2 = 10x + -10x + 5x2 + -5x2

Combine like terms: 10x + -10x = 0
90 + -10x + -5x2 = 0 + 5x2 + -5x2
90 + -10x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
90 + -10x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(18 + -2x + -1x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(18 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
18 + -2x + -1x2 = 0

Solving
18 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-18 + 2x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 2x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 2x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 2x + x2 = 0 + 18
2x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
2x + x2 = 18

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 18 + 1

Reorder the terms:
1 + 2x + x2 = 18 + 1

Combine like terms: 18 + 1 = 19
1 + 2x + x2 = 19

Factor a perfect square on the left side:
(x + 1)(x + 1) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + 1) equal to 4.358898944 and -4.358898944.


Subproblem 1
x + 1 = 4.358898944

Simplifying
x + 1 = 4.358898944

Reorder the terms:
1 + x = 4.358898944

Solving
1 + x = 4.358898944

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 4.358898944 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.358898944 + -1
x = 4.358898944 + -1

Combine like terms: 4.358898944 + -1 = 3.358898944
x = 3.358898944

Simplifying
x = 3.358898944


Subproblem 2
x + 1 = -4.358898944

Simplifying
x + 1 = -4.358898944

Reorder the terms:
1 + x = -4.358898944

Solving
1 + x = -4.358898944

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -4.358898944 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.358898944 + -1
x = -4.358898944 + -1

Combine like terms: -4.358898944 + -1 = -5.358898944
x = -5.358898944

Simplifying
x = -5.358898944


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.358898944, -5.358898944}
Solution
x = {3.358898944, -5.358898944}

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