16r^2=-13r+20-5r^2

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Solution for 16r^2=-13r+20-5r^2 equation:


Simplifying
16r2 = -13r + 20 + -5r2

Reorder the terms:
16r2 = 20 + -13r + -5r2

Solving
16r2 = 20 + -13r + -5r2

Solving for variable 'r'.

Reorder the terms:
-20 + 13r + 16r2 + 5r2 = 20 + -13r + -5r2 + -20 + 13r + 5r2

Combine like terms: 16r2 + 5r2 = 21r2
-20 + 13r + 21r2 = 20 + -13r + -5r2 + -20 + 13r + 5r2

Reorder the terms:
-20 + 13r + 21r2 = 20 + -20 + -13r + 13r + -5r2 + 5r2

Combine like terms: 20 + -20 = 0
-20 + 13r + 21r2 = 0 + -13r + 13r + -5r2 + 5r2
-20 + 13r + 21r2 = -13r + 13r + -5r2 + 5r2

Combine like terms: -13r + 13r = 0
-20 + 13r + 21r2 = 0 + -5r2 + 5r2
-20 + 13r + 21r2 = -5r2 + 5r2

Combine like terms: -5r2 + 5r2 = 0
-20 + 13r + 21r2 = 0

Factor a trinomial.
(-4 + -3r)(5 + -7r) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(5 + -7r)' equal to zero and attempt to solve: Simplifying 5 + -7r = 0 Solving 5 + -7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -7r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7r = 0 + -5 -7r = 0 + -5 Combine like terms: 0 + -5 = -5 -7r = -5 Divide each side by '-7'. r = 0.7142857143 Simplifying r = 0.7142857143

Solution

r = {-1.333333333, 0.7142857143}

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