4c(c-3)=6-2c

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Solution for 4c(c-3)=6-2c equation:


Simplifying
4c(c + -3) = 6 + -2c

Reorder the terms:
4c(-3 + c) = 6 + -2c
(-3 * 4c + c * 4c) = 6 + -2c
(-12c + 4c2) = 6 + -2c

Solving
-12c + 4c2 = 6 + -2c

Solving for variable 'c'.

Reorder the terms:
-6 + -12c + 2c + 4c2 = 6 + -2c + -6 + 2c

Combine like terms: -12c + 2c = -10c
-6 + -10c + 4c2 = 6 + -2c + -6 + 2c

Reorder the terms:
-6 + -10c + 4c2 = 6 + -6 + -2c + 2c

Combine like terms: 6 + -6 = 0
-6 + -10c + 4c2 = 0 + -2c + 2c
-6 + -10c + 4c2 = -2c + 2c

Combine like terms: -2c + 2c = 0
-6 + -10c + 4c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5c + 2c2) = 0

Factor a trinomial.
2((-1 + -2c)(3 + -1c)) = 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 '(3 + -1c)' equal to zero and attempt to solve: Simplifying 3 + -1c = 0 Solving 3 + -1c = 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 + -1c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1c = 0 + -3 -1c = 0 + -3 Combine like terms: 0 + -3 = -3 -1c = -3 Divide each side by '-1'. c = 3 Simplifying c = 3

Solution

c = {-0.5, 3}

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