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

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


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

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

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

Multiply (5 + 3c) * (3 + c)
(5(3 + c) + 3c * (3 + c)) = 7
((3 * 5 + c * 5) + 3c * (3 + c)) = 7
((15 + 5c) + 3c * (3 + c)) = 7
(15 + 5c + (3 * 3c + c * 3c)) = 7
(15 + 5c + (9c + 3c2)) = 7

Combine like terms: 5c + 9c = 14c
(15 + 14c + 3c2) = 7

Solving
15 + 14c + 3c2 = 7

Solving for variable 'c'.

Reorder the terms:
15 + -7 + 14c + 3c2 = 7 + -7

Combine like terms: 15 + -7 = 8
8 + 14c + 3c2 = 7 + -7

Combine like terms: 7 + -7 = 0
8 + 14c + 3c2 = 0

Factor a trinomial.
(4 + c)(2 + 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 '(2 + 3c)' equal to zero and attempt to solve: Simplifying 2 + 3c = 0 Solving 2 + 3c = 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 + 3c = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3c = 0 + -2 3c = 0 + -2 Combine like terms: 0 + -2 = -2 3c = -2 Divide each side by '3'. c = -0.6666666667 Simplifying c = -0.6666666667

Solution

c = {-4, -0.6666666667}

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