4w^2-4w=24

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Solution for 4w^2-4w=24 equation:


Simplifying
4w2 + -4w = 24

Reorder the terms:
-4w + 4w2 = 24

Solving
-4w + 4w2 = 24

Solving for variable 'w'.

Reorder the terms:
-24 + -4w + 4w2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -4w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -1w + w2) = 0

Factor a trinomial.
4((-2 + -1w)(3 + -1w)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-2 + -1w)' equal to zero and attempt to solve: Simplifying -2 + -1w = 0 Solving -2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1w = 0 + 2 -1w = 0 + 2 Combine like terms: 0 + 2 = 2 -1w = 2 Divide each side by '-1'. w = -2 Simplifying w = -2

Subproblem 2

Set the factor '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3

Solution

w = {-2, 3}

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