2x*(5x+4)=5*(x+1)

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Solution for 2x*(5x+4)=5*(x+1) equation: 


Simplifying
2x(5x + 4) = 5(x + 1)

Reorder the terms:
2x(4 + 5x) = 5(x + 1)
(4 * 2x + 5x * 2x) = 5(x + 1)
(8x + 10x2) = 5(x + 1)

Reorder the terms:
8x + 10x2 = 5(1 + x)
8x + 10x2 = (1 * 5 + x * 5)
8x + 10x2 = (5 + 5x)

Solving
8x + 10x2 = 5 + 5x

Solving for variable 'x'.

Reorder the terms:
-5 + 8x + -5x + 10x2 = 5 + 5x + -5 + -5x

Combine like terms: 8x + -5x = 3x
-5 + 3x + 10x2 = 5 + 5x + -5 + -5x

Reorder the terms:
-5 + 3x + 10x2 = 5 + -5 + 5x + -5x

Combine like terms: 5 + -5 = 0
-5 + 3x + 10x2 = 0 + 5x + -5x
-5 + 3x + 10x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-5 + 3x + 10x2 = 0

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

Divide each side by '10'.
-0.5 + 0.3x + x2 = 0.0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.3x + 0.5 + x2 = 0.0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.3x + x2 = 0.0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.3x + x2 = 0.0 + 0.5
0.3x + x2 = 0.0 + 0.5

Combine like terms: 0.0 + 0.5 = 0.5
0.3x + x2 = 0.5

The x term is 0.3x.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3x + 0.0225 + x2 = 0.5 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 0.5 + 0.0225

Combine like terms: 0.5 + 0.0225 = 0.5225
0.0225 + 0.3x + x2 = 0.5225

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 0.5225

Calculate the square root of the right side: 0.722841615

Break this problem into two subproblems by setting 
(x + 0.15) equal to 0.722841615 and -0.722841615.


Subproblem 1
x + 0.15 = 0.722841615

Simplifying
x + 0.15 = 0.722841615

Reorder the terms:
0.15 + x = 0.722841615

Solving
0.15 + x = 0.722841615

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = 0.722841615 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = 0.722841615 + -0.15
x = 0.722841615 + -0.15

Combine like terms: 0.722841615 + -0.15 = 0.572841615
x = 0.572841615

Simplifying
x = 0.572841615


Subproblem 2
x + 0.15 = -0.722841615

Simplifying
x + 0.15 = -0.722841615

Reorder the terms:
0.15 + x = -0.722841615

Solving
0.15 + x = -0.722841615

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = -0.722841615 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = -0.722841615 + -0.15
x = -0.722841615 + -0.15

Combine like terms: -0.722841615 + -0.15 = -0.872841615
x = -0.872841615

Simplifying
x = -0.872841615


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.572841615, -0.872841615}

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