3(4c-7)4(4c+1)=0

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Solution for 3(4c-7)4(4c+1)=0 equation: 


Simplifying
3(4c + -7) * 4(4c + 1) = 0

Reorder the terms:
3(-7 + 4c) * 4(4c + 1) = 0

Reorder the terms:
3(-7 + 4c) * 4(1 + 4c) = 0

Reorder the terms for easier multiplication:
3 * 4(-7 + 4c)(1 + 4c) = 0

Multiply 3 * 4
12(-7 + 4c)(1 + 4c) = 0

Multiply (-7 + 4c) * (1 + 4c)
12(-7(1 + 4c) + 4c * (1 + 4c)) = 0
12((1 * -7 + 4c * -7) + 4c * (1 + 4c)) = 0
12((-7 + -28c) + 4c * (1 + 4c)) = 0
12(-7 + -28c + (1 * 4c + 4c * 4c)) = 0
12(-7 + -28c + (4c + 16c2)) = 0

Combine like terms: -28c + 4c = -24c
12(-7 + -24c + 16c2) = 0
(-7 * 12 + -24c * 12 + 16c2 * 12) = 0
(-84 + -288c + 192c2) = 0

Solving
-84 + -288c + 192c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-7 + -24c + 16c2) = 0

Factor a trinomial.
12((-1 + -4c)(7 + -4c)) = 0

Ignore the factor 12.

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

Simplifying
-1 + -4c = 0

Solving
-1 + -4c = 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 + -4c = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4c = 0 + 1
-4c = 0 + 1

Combine like terms: 0 + 1 = 1
-4c = 1

Divide each side by '-4'.
c = -0.25

Simplifying
c = -0.25

Subproblem 2
Set the factor '(7 + -4c)' equal to zero and attempt to solve:

Simplifying
7 + -4c = 0

Solving
7 + -4c = 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 + -4c = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4c = 0 + -7
-4c = 0 + -7

Combine like terms: 0 + -7 = -7
-4c = -7

Divide each side by '-4'.
c = 1.75

Simplifying
c = 1.75
Solution
c = {-0.25, 1.75}

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