(0.3c+0.3)(c+0.7)=

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Solution for (0.3c+0.3)(c+0.7)= equation: 


Simplifying
(0.3c + 0.3)(c + 0.7) = 0

Reorder the terms:
(0.3 + 0.3c)(c + 0.7) = 0

Reorder the terms:
(0.3 + 0.3c)(0.7 + c) = 0

Multiply (0.3 + 0.3c) * (0.7 + c)
(0.3(0.7 + c) + 0.3c * (0.7 + c)) = 0
((0.7 * 0.3 + c * 0.3) + 0.3c * (0.7 + c)) = 0
((0.21 + 0.3c) + 0.3c * (0.7 + c)) = 0
(0.21 + 0.3c + (0.7 * 0.3c + c * 0.3c)) = 0
(0.21 + 0.3c + (0.21c + 0.3c2)) = 0

Combine like terms: 0.3c + 0.21c = 0.51c
(0.21 + 0.51c + 0.3c2) = 0

Solving
0.21 + 0.51c + 0.3c2 = 0

Solving for variable 'c'.

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

Divide each side by '0.3'.
0.7 + 1.7c + c2 = 0

Move the constant term to the right:

Add '-0.7' to each side of the equation.
0.7 + 1.7c + -0.7 + c2 = 0 + -0.7

Reorder the terms:
0.7 + -0.7 + 1.7c + c2 = 0 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + 1.7c + c2 = 0 + -0.7
1.7c + c2 = 0 + -0.7

Combine like terms: 0 + -0.7 = -0.7
1.7c + c2 = -0.7

The c term is 1.7c.  Take half its coefficient (0.85).
Square it (0.7225) and add it to both sides.

Add '0.7225' to each side of the equation.
1.7c + 0.7225 + c2 = -0.7 + 0.7225

Reorder the terms:
0.7225 + 1.7c + c2 = -0.7 + 0.7225

Combine like terms: -0.7 + 0.7225 = 0.0225
0.7225 + 1.7c + c2 = 0.0225

Factor a perfect square on the left side:
(c + 0.85)(c + 0.85) = 0.0225

Calculate the square root of the right side: 0.15

Break this problem into two subproblems by setting 
(c + 0.85) equal to 0.15 and -0.15.


Subproblem 1
c + 0.85 = 0.15

Simplifying
c + 0.85 = 0.15

Reorder the terms:
0.85 + c = 0.15

Solving
0.85 + c = 0.15

Solving for variable 'c'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + c = 0.15 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + c = 0.15 + -0.85
c = 0.15 + -0.85

Combine like terms: 0.15 + -0.85 = -0.7
c = -0.7

Simplifying
c = -0.7


Subproblem 2
c + 0.85 = -0.15

Simplifying
c + 0.85 = -0.15

Reorder the terms:
0.85 + c = -0.15

Solving
0.85 + c = -0.15

Solving for variable 'c'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + c = -0.15 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + c = -0.15 + -0.85
c = -0.15 + -0.85

Combine like terms: -0.15 + -0.85 = -1
c = -1

Simplifying
c = -1


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.7, -1}

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