150r^2=210r+48

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Solution for 150r^2=210r+48 equation:


Simplifying
150r2 = 210r + 48

Reorder the terms:
150r2 = 48 + 210r

Solving
150r2 = 48 + 210r

Solving for variable 'r'.

Reorder the terms:
-48 + -210r + 150r2 = 48 + 210r + -48 + -210r

Reorder the terms:
-48 + -210r + 150r2 = 48 + -48 + 210r + -210r

Combine like terms: 48 + -48 = 0
-48 + -210r + 150r2 = 0 + 210r + -210r
-48 + -210r + 150r2 = 210r + -210r

Combine like terms: 210r + -210r = 0
-48 + -210r + 150r2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-8 + -35r + 25r2) = 0

Factor a trinomial.
6((-1 + -5r)(8 + -5r)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-1 + -5r)' equal to zero and attempt to solve: Simplifying -1 + -5r = 0 Solving -1 + -5r = 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 + -5r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5r = 0 + 1 -5r = 0 + 1 Combine like terms: 0 + 1 = 1 -5r = 1 Divide each side by '-5'. r = -0.2 Simplifying r = -0.2

Subproblem 2

Set the factor '(8 + -5r)' equal to zero and attempt to solve: Simplifying 8 + -5r = 0 Solving 8 + -5r = 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 + -5r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5r = 0 + -8 -5r = 0 + -8 Combine like terms: 0 + -8 = -8 -5r = -8 Divide each side by '-5'. r = 1.6 Simplifying r = 1.6

Solution

r = {-0.2, 1.6}

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