24r^2-8=3r^2+53r

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Solution for 24r^2-8=3r^2+53r equation:


Simplifying
24r2 + -8 = 3r2 + 53r

Reorder the terms:
-8 + 24r2 = 3r2 + 53r

Reorder the terms:
-8 + 24r2 = 53r + 3r2

Solving
-8 + 24r2 = 53r + 3r2

Solving for variable 'r'.

Reorder the terms:
-8 + -53r + 24r2 + -3r2 = 53r + 3r2 + -53r + -3r2

Combine like terms: 24r2 + -3r2 = 21r2
-8 + -53r + 21r2 = 53r + 3r2 + -53r + -3r2

Reorder the terms:
-8 + -53r + 21r2 = 53r + -53r + 3r2 + -3r2

Combine like terms: 53r + -53r = 0
-8 + -53r + 21r2 = 0 + 3r2 + -3r2
-8 + -53r + 21r2 = 3r2 + -3r2

Combine like terms: 3r2 + -3r2 = 0
-8 + -53r + 21r2 = 0

Factor a trinomial.
(-1 + -7r)(8 + -3r) = 0

Subproblem 1

Set the factor '(-1 + -7r)' equal to zero and attempt to solve: Simplifying -1 + -7r = 0 Solving -1 + -7r = 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 + -7r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7r = 0 + 1 -7r = 0 + 1 Combine like terms: 0 + 1 = 1 -7r = 1 Divide each side by '-7'. r = -0.1428571429 Simplifying r = -0.1428571429

Subproblem 2

Set the factor '(8 + -3r)' equal to zero and attempt to solve: Simplifying 8 + -3r = 0 Solving 8 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3r = 0 + -8 -3r = 0 + -8 Combine like terms: 0 + -8 = -8 -3r = -8 Divide each side by '-3'. r = 2.666666667 Simplifying r = 2.666666667

Solution

r = {-0.1428571429, 2.666666667}

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