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

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

Simplifying
0 = (5c + -2)(7c + 3)

Reorder the terms:
0 = (-2 + 5c)(7c + 3)

Reorder the terms:
0 = (-2 + 5c)(3 + 7c)

Multiply (-2 + 5c) * (3 + 7c)
0 = (-2(3 + 7c) + 5c * (3 + 7c))
0 = ((3 * -2 + 7c * -2) + 5c * (3 + 7c))
0 = ((-6 + -14c) + 5c * (3 + 7c))
0 = (-6 + -14c + (3 * 5c + 7c * 5c))
0 = (-6 + -14c + (15c + 35c2))

Combine like terms: -14c + 15c = 1c
0 = (-6 + 1c + 35c2)

Solving
0 = -6 + 1c + 35c2

Solving for variable 'c'.

Combine like terms: 0 + 6 = 6
6 + -1c + -35c2 = -6 + 1c + 35c2 + 6 + -1c + -35c2

Reorder the terms:
6 + -1c + -35c2 = -6 + 6 + 1c + -1c + 35c2 + -35c2

Combine like terms: -6 + 6 = 0
6 + -1c + -35c2 = 0 + 1c + -1c + 35c2 + -35c2
6 + -1c + -35c2 = 1c + -1c + 35c2 + -35c2

Combine like terms: 1c + -1c = 0
6 + -1c + -35c2 = 0 + 35c2 + -35c2
6 + -1c + -35c2 = 35c2 + -35c2

Combine like terms: 35c2 + -35c2 = 0
6 + -1c + -35c2 = 0

Factor a trinomial.
(2 + -5c)(3 + 7c) = 0

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

Simplifying
2 + -5c = 0

Solving
2 + -5c = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5c = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5c = 0 + -2
-5c = 0 + -2

Combine like terms: 0 + -2 = -2
-5c = -2

Divide each side by '-5'.
c = 0.4

Simplifying
c = 0.4
Subproblem 2
Set the factor '(3 + 7c)' equal to zero and attempt to solve:

Simplifying
3 + 7c = 0

Solving
3 + 7c = 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 + 7c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7c = 0 + -3
7c = 0 + -3

Combine like terms: 0 + -3 = -3
7c = -3

Divide each side by '7'.
c = -0.4285714286

Simplifying
c = -0.4285714286
Solution
c = {0.4, -0.4285714286}