5(2c+7)-3c=7(c+5)c

Solution for 5(2c+7)-3c=7(c+5)c equation:

Simplifying
5(2c + 7) + -3c = 7(c + 5) * c

Reorder the terms:
5(7 + 2c) + -3c = 7(c + 5) * c
(7 * 5 + 2c * 5) + -3c = 7(c + 5) * c
(35 + 10c) + -3c = 7(c + 5) * c

Combine like terms: 10c + -3c = 7c
35 + 7c = 7(c + 5) * c

Reorder the terms:
35 + 7c = 7(5 + c) * c

Reorder the terms for easier multiplication:
35 + 7c = 7c(5 + c)
35 + 7c = (5 * 7c + c * 7c)
35 + 7c = (35c + 7c2)

Solving
35 + 7c = 35c + 7c2

Solving for variable 'c'.

Combine like terms: 7c + -35c = -28c
35 + -28c + -7c2 = 35c + 7c2 + -35c + -7c2

Reorder the terms:
35 + -28c + -7c2 = 35c + -35c + 7c2 + -7c2

Combine like terms: 35c + -35c = 0
35 + -28c + -7c2 = 0 + 7c2 + -7c2
35 + -28c + -7c2 = 7c2 + -7c2

Combine like terms: 7c2 + -7c2 = 0
35 + -28c + -7c2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(5 + -4c + -1c2) = 0

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

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

Simplifying
1 + -1c = 0

Solving
1 + -1c = 0

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

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

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

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

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

Simplifying
c = 1
Subproblem 2
Set the factor '(5 + c)' equal to zero and attempt to solve:

Simplifying
5 + c = 0

Solving
5 + c = 0

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

Add '-5' to each side of the equation.
5 + -5 + c = 0 + -5

Combine like terms: 5 + -5 = 0
0 + c = 0 + -5
c = 0 + -5

Combine like terms: 0 + -5 = -5
c = -5

Simplifying
c = -5
Solution
c = {1, -5}