(12c+7)(5c-15)=0

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Solution for (12c+7)(5c-15)=0 equation: 


Simplifying
(12c + 7)(5c + -15) = 0

Reorder the terms:
(7 + 12c)(5c + -15) = 0

Reorder the terms:
(7 + 12c)(-15 + 5c) = 0

Multiply (7 + 12c) * (-15 + 5c)
(7(-15 + 5c) + 12c * (-15 + 5c)) = 0
((-15 * 7 + 5c * 7) + 12c * (-15 + 5c)) = 0
((-105 + 35c) + 12c * (-15 + 5c)) = 0
(-105 + 35c + (-15 * 12c + 5c * 12c)) = 0
(-105 + 35c + (-180c + 60c2)) = 0

Combine like terms: 35c + -180c = -145c
(-105 + -145c + 60c2) = 0

Solving
-105 + -145c + 60c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + -29c + 12c2) = 0

Factor a trinomial.
5((-7 + -12c)(3 + -1c)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -12c)' equal to zero and attempt to solve:

Simplifying
-7 + -12c = 0

Solving
-7 + -12c = 0

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

Add '7' to each side of the equation.
-7 + 7 + -12c = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -12c = 0 + 7
-12c = 0 + 7

Combine like terms: 0 + 7 = 7
-12c = 7

Divide each side by '-12'.
c = -0.5833333333

Simplifying
c = -0.5833333333

Subproblem 2
Set the factor '(3 + -1c)' equal to zero and attempt to solve:

Simplifying
3 + -1c = 0

Solving
3 + -1c = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1c = 0 + -3
-1c = 0 + -3

Combine like terms: 0 + -3 = -3
-1c = -3

Divide each side by '-1'.
c = 3

Simplifying
c = 3
Solution
c = {-0.5833333333, 3}

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