(4r+2)(5r-4)=

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Solution for (4r+2)(5r-4)= equation:


Simplifying
(4r + 2)(5r + -4) = 0

Reorder the terms:
(2 + 4r)(5r + -4) = 0

Reorder the terms:
(2 + 4r)(-4 + 5r) = 0

Multiply (2 + 4r) * (-4 + 5r)
(2(-4 + 5r) + 4r * (-4 + 5r)) = 0
((-4 * 2 + 5r * 2) + 4r * (-4 + 5r)) = 0
((-8 + 10r) + 4r * (-4 + 5r)) = 0
(-8 + 10r + (-4 * 4r + 5r * 4r)) = 0
(-8 + 10r + (-16r + 20r2)) = 0

Combine like terms: 10r + -16r = -6r
(-8 + -6r + 20r2) = 0

Solving
-8 + -6r + 20r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -3r + 10r2) = 0

Factor a trinomial.
2((-1 + -2r)(4 + -5r)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -2r)' equal to zero and attempt to solve: Simplifying -1 + -2r = 0 Solving -1 + -2r = 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 + -2r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2r = 0 + 1 -2r = 0 + 1 Combine like terms: 0 + 1 = 1 -2r = 1 Divide each side by '-2'. r = -0.5 Simplifying r = -0.5

Subproblem 2

Set the factor '(4 + -5r)' equal to zero and attempt to solve: Simplifying 4 + -5r = 0 Solving 4 + -5r = 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 + -5r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5r = 0 + -4 -5r = 0 + -4 Combine like terms: 0 + -4 = -4 -5r = -4 Divide each side by '-5'. r = 0.8 Simplifying r = 0.8

Solution

r = {-0.5, 0.8}

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