(5-c)(3c-5)=7

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Solution for (5-c)(3c-5)=7 equation:


Simplifying
(5 + -1c)(3c + -5) = 7

Reorder the terms:
(5 + -1c)(-5 + 3c) = 7

Multiply (5 + -1c) * (-5 + 3c)
(5(-5 + 3c) + -1c * (-5 + 3c)) = 7
((-5 * 5 + 3c * 5) + -1c * (-5 + 3c)) = 7
((-25 + 15c) + -1c * (-5 + 3c)) = 7
(-25 + 15c + (-5 * -1c + 3c * -1c)) = 7
(-25 + 15c + (5c + -3c2)) = 7

Combine like terms: 15c + 5c = 20c
(-25 + 20c + -3c2) = 7

Solving
-25 + 20c + -3c2 = 7

Solving for variable 'c'.

Reorder the terms:
-25 + -7 + 20c + -3c2 = 7 + -7

Combine like terms: -25 + -7 = -32
-32 + 20c + -3c2 = 7 + -7

Combine like terms: 7 + -7 = 0
-32 + 20c + -3c2 = 0

Factor a trinomial.
(-4 + c)(8 + -3c) = 0


Subproblem 1
Set the factor '(-4 + c)' equal to zero and attempt to solve:

Simplifying
-4 + c = 0

Solving
-4 + c = 0

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

Add '4' to each side of the equation.
-4 + 4 + c = 0 + 4

Combine like terms: -4 + 4 = 0
0 + c = 0 + 4
c = 0 + 4

Combine like terms: 0 + 4 = 4
c = 4

Simplifying
c = 4

Subproblem 2
Set the factor '(8 + -3c)' equal to zero and attempt to solve:

Simplifying
8 + -3c = 0

Solving
8 + -3c = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3c = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3c = 0 + -8
-3c = 0 + -8

Combine like terms: 0 + -8 = -8
-3c = -8

Divide each side by '-3'.
c = 2.666666667

Simplifying
c = 2.666666667
Solution
c = {4, 2.666666667}

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