(1+g)*(.15-g)=

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Solution for (1+g)*(.15-g)= equation: 


Simplifying
(1 + g)(0.15 + -1g) = 0

Multiply (1 + g) * (0.15 + -1g)
(1(0.15 + -1g) + g(0.15 + -1g)) = 0
((0.15 * 1 + -1g * 1) + g(0.15 + -1g)) = 0
((0.15 + -1g) + g(0.15 + -1g)) = 0
(0.15 + -1g + (0.15 * g + -1g * g)) = 0
(0.15 + -1g + (0.15g + -1g2)) = 0

Combine like terms: -1g + 0.15g = -0.85g
(0.15 + -0.85g + -1g2) = 0

Solving
0.15 + -0.85g + -1g2 = 0

Solving for variable 'g'.

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

Divide each side by '-1'.
-0.15 + 0.85g + g2 = 0

Move the constant term to the right:

Add '0.15' to each side of the equation.
-0.15 + 0.85g + 0.15 + g2 = 0 + 0.15

Reorder the terms:
-0.15 + 0.15 + 0.85g + g2 = 0 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + 0.85g + g2 = 0 + 0.15
0.85g + g2 = 0 + 0.15

Combine like terms: 0 + 0.15 = 0.15
0.85g + g2 = 0.15

The g term is 0.85g.  Take half its coefficient (0.425).
Square it (0.180625) and add it to both sides.

Add '0.180625' to each side of the equation.
0.85g + 0.180625 + g2 = 0.15 + 0.180625

Reorder the terms:
0.180625 + 0.85g + g2 = 0.15 + 0.180625

Combine like terms: 0.15 + 0.180625 = 0.330625
0.180625 + 0.85g + g2 = 0.330625

Factor a perfect square on the left side:
(g + 0.425)(g + 0.425) = 0.330625

Calculate the square root of the right side: 0.575

Break this problem into two subproblems by setting 
(g + 0.425) equal to 0.575 and -0.575.


Subproblem 1
g + 0.425 = 0.575

Simplifying
g + 0.425 = 0.575

Reorder the terms:
0.425 + g = 0.575

Solving
0.425 + g = 0.575

Solving for variable 'g'.

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

Add '-0.425' to each side of the equation.
0.425 + -0.425 + g = 0.575 + -0.425

Combine like terms: 0.425 + -0.425 = 0.000
0.000 + g = 0.575 + -0.425
g = 0.575 + -0.425

Combine like terms: 0.575 + -0.425 = 0.15
g = 0.15

Simplifying
g = 0.15


Subproblem 2
g + 0.425 = -0.575

Simplifying
g + 0.425 = -0.575

Reorder the terms:
0.425 + g = -0.575

Solving
0.425 + g = -0.575

Solving for variable 'g'.

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

Add '-0.425' to each side of the equation.
0.425 + -0.425 + g = -0.575 + -0.425

Combine like terms: 0.425 + -0.425 = 0.000
0.000 + g = -0.575 + -0.425
g = -0.575 + -0.425

Combine like terms: -0.575 + -0.425 = -1
g = -1

Simplifying
g = -1


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {0.15, -1}

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