(4w-6f)*(4w+5f)=

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Solution for (4w-6f)*(4w+5f)= equation:


Simplifying
(4w + -6f)(4w + 5f) = 0

Reorder the terms:
(-6f + 4w)(4w + 5f) = 0

Reorder the terms:
(-6f + 4w)(5f + 4w) = 0

Multiply (-6f + 4w) * (5f + 4w)
(-6f * (5f + 4w) + 4w * (5f + 4w)) = 0
((5f * -6f + 4w * -6f) + 4w * (5f + 4w)) = 0

Reorder the terms:
((-24fw + -30f2) + 4w * (5f + 4w)) = 0
((-24fw + -30f2) + 4w * (5f + 4w)) = 0
(-24fw + -30f2 + (5f * 4w + 4w * 4w)) = 0
(-24fw + -30f2 + (20fw + 16w2)) = 0

Reorder the terms:
(-24fw + 20fw + -30f2 + 16w2) = 0

Combine like terms: -24fw + 20fw = -4fw
(-4fw + -30f2 + 16w2) = 0

Solving
-4fw + -30f2 + 16w2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2fw + -15f2 + 8w2) = 0

Factor a trinomial.
2((-5f + -4w)(3f + -2w)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5f + -4w)' equal to zero and attempt to solve: Simplifying -5f + -4w = 0 Solving -5f + -4w = 0 Move all terms containing f to the left, all other terms to the right. Add '4w' to each side of the equation. -5f + -4w + 4w = 0 + 4w Combine like terms: -4w + 4w = 0 -5f + 0 = 0 + 4w -5f = 0 + 4w Remove the zero: -5f = 4w Divide each side by '-5'. f = -0.8w Simplifying f = -0.8w

Subproblem 2

Set the factor '(3f + -2w)' equal to zero and attempt to solve: Simplifying 3f + -2w = 0 Solving 3f + -2w = 0 Move all terms containing f to the left, all other terms to the right. Add '2w' to each side of the equation. 3f + -2w + 2w = 0 + 2w Combine like terms: -2w + 2w = 0 3f + 0 = 0 + 2w 3f = 0 + 2w Remove the zero: 3f = 2w Divide each side by '3'. f = 0.6666666667w Simplifying f = 0.6666666667w

Solution

f = {-0.8w, 0.6666666667w}

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