(0.4c+0.2)(c+0.7)=

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Solution for (0.4c+0.2)(c+0.7)= equation: 


Simplifying
(0.4c + 0.2)(c + 0.7) = 0

Reorder the terms:
(0.2 + 0.4c)(c + 0.7) = 0

Reorder the terms:
(0.2 + 0.4c)(0.7 + c) = 0

Multiply (0.2 + 0.4c) * (0.7 + c)
(0.2(0.7 + c) + 0.4c * (0.7 + c)) = 0
((0.7 * 0.2 + c * 0.2) + 0.4c * (0.7 + c)) = 0
((0.14 + 0.2c) + 0.4c * (0.7 + c)) = 0
(0.14 + 0.2c + (0.7 * 0.4c + c * 0.4c)) = 0
(0.14 + 0.2c + (0.28c + 0.4c2)) = 0

Combine like terms: 0.2c + 0.28c = 0.48c
(0.14 + 0.48c + 0.4c2) = 0

Solving
0.14 + 0.48c + 0.4c2 = 0

Solving for variable 'c'.

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

Divide each side by '0.4'.
0.35 + 1.2c + c2 = 0

Move the constant term to the right:

Add '-0.35' to each side of the equation.
0.35 + 1.2c + -0.35 + c2 = 0 + -0.35

Reorder the terms:
0.35 + -0.35 + 1.2c + c2 = 0 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + 1.2c + c2 = 0 + -0.35
1.2c + c2 = 0 + -0.35

Combine like terms: 0 + -0.35 = -0.35
1.2c + c2 = -0.35

The c term is 1.2c.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2c + 0.36 + c2 = -0.35 + 0.36

Reorder the terms:
0.36 + 1.2c + c2 = -0.35 + 0.36

Combine like terms: -0.35 + 0.36 = 0.01
0.36 + 1.2c + c2 = 0.01

Factor a perfect square on the left side:
(c + 0.6)(c + 0.6) = 0.01

Calculate the square root of the right side: 0.1

Break this problem into two subproblems by setting 
(c + 0.6) equal to 0.1 and -0.1.


Subproblem 1
c + 0.6 = 0.1

Simplifying
c + 0.6 = 0.1

Reorder the terms:
0.6 + c = 0.1

Solving
0.6 + c = 0.1

Solving for variable 'c'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + c = 0.1 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + c = 0.1 + -0.6
c = 0.1 + -0.6

Combine like terms: 0.1 + -0.6 = -0.5
c = -0.5

Simplifying
c = -0.5


Subproblem 2
c + 0.6 = -0.1

Simplifying
c + 0.6 = -0.1

Reorder the terms:
0.6 + c = -0.1

Solving
0.6 + c = -0.1

Solving for variable 'c'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + c = -0.1 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + c = -0.1 + -0.6
c = -0.1 + -0.6

Combine like terms: -0.1 + -0.6 = -0.7
c = -0.7

Simplifying
c = -0.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.5, -0.7}

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