4r(3r-4)(4r-1)=0

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Solution for 4r(3r-4)(4r-1)=0 equation:


Simplifying
4r(3r + -4)(4r + -1) = 0

Reorder the terms:
4r(-4 + 3r)(4r + -1) = 0

Reorder the terms:
4r(-4 + 3r)(-1 + 4r) = 0

Multiply (-4 + 3r) * (-1 + 4r)
4r(-4(-1 + 4r) + 3r * (-1 + 4r)) = 0
4r((-1 * -4 + 4r * -4) + 3r * (-1 + 4r)) = 0
4r((4 + -16r) + 3r * (-1 + 4r)) = 0
4r(4 + -16r + (-1 * 3r + 4r * 3r)) = 0
4r(4 + -16r + (-3r + 12r2)) = 0

Combine like terms: -16r + -3r = -19r
4r(4 + -19r + 12r2) = 0
(4 * 4r + -19r * 4r + 12r2 * 4r) = 0
(16r + -76r2 + 48r3) = 0

Solving
16r + -76r2 + 48r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4r'.
4r(4 + -19r + 12r2) = 0

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

Ignore the factor 4.

Subproblem 1

Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0

Subproblem 2

Set the factor '(1 + -4r)' equal to zero and attempt to solve: Simplifying 1 + -4r = 0 Solving 1 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4r = 0 + -1 -4r = 0 + -1 Combine like terms: 0 + -1 = -1 -4r = -1 Divide each side by '-4'. r = 0.25 Simplifying r = 0.25

Subproblem 3

Set the factor '(4 + -3r)' equal to zero and attempt to solve: Simplifying 4 + -3r = 0 Solving 4 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3r = 0 + -4 -3r = 0 + -4 Combine like terms: 0 + -4 = -4 -3r = -4 Divide each side by '-3'. r = 1.333333333 Simplifying r = 1.333333333

Solution

r = {0, 0.25, 1.333333333}

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