(4c+2)(2c+-7)=0

Solution for (4c+2)(2c+-7)=0 equation:

Simplifying
(4c + 2)(2c + -7) = 0

Reorder the terms:
(2 + 4c)(2c + -7) = 0

Reorder the terms:
(2 + 4c)(-7 + 2c) = 0

Multiply (2 + 4c) * (-7 + 2c)
(2(-7 + 2c) + 4c * (-7 + 2c)) = 0
((-7 * 2 + 2c * 2) + 4c * (-7 + 2c)) = 0
((-14 + 4c) + 4c * (-7 + 2c)) = 0
(-14 + 4c + (-7 * 4c + 2c * 4c)) = 0
(-14 + 4c + (-28c + 8c2)) = 0

Combine like terms: 4c + -28c = -24c
(-14 + -24c + 8c2) = 0

Solving
-14 + -24c + 8c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -12c + 4c2) = 0

Factor a trinomial.
2((-1 + -2c)(7 + -2c)) = 0

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

Simplifying
-1 + -2c = 0

Solving
-1 + -2c = 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 + -2c = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2c = 0 + 1
-2c = 0 + 1

Combine like terms: 0 + 1 = 1
-2c = 1

Divide each side by '-2'.
c = -0.5

Simplifying
c = -0.5
Subproblem 2
Set the factor '(7 + -2c)' equal to zero and attempt to solve:

Simplifying
7 + -2c = 0

Solving
7 + -2c = 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 + -2c = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2c = 0 + -7
-2c = 0 + -7

Combine like terms: 0 + -7 = -7
-2c = -7

Divide each side by '-2'.
c = 3.5

Simplifying
c = 3.5
Solution
c = {-0.5, 3.5}