20r^2+7=45r+7

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Solution for 20r^2+7=45r+7 equation:


Simplifying
20r2 + 7 = 45r + 7

Reorder the terms:
7 + 20r2 = 45r + 7

Reorder the terms:
7 + 20r2 = 7 + 45r

Add '-7' to each side of the equation.
7 + -7 + 20r2 = 7 + -7 + 45r

Combine like terms: 7 + -7 = 0
0 + 20r2 = 7 + -7 + 45r
20r2 = 7 + -7 + 45r

Combine like terms: 7 + -7 = 0
20r2 = 0 + 45r
20r2 = 45r

Solving
20r2 = 45r

Solving for variable 'r'.

Reorder the terms:
-45r + 20r2 = 45r + -45r

Combine like terms: 45r + -45r = 0
-45r + 20r2 = 0

Factor out the Greatest Common Factor (GCF), '5r'.
5r(-9 + 4r) = 0

Ignore the factor 5.

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 '(-9 + 4r)' equal to zero and attempt to solve: Simplifying -9 + 4r = 0 Solving -9 + 4r = 0 Move all terms containing r to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 4r = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4r = 0 + 9 4r = 0 + 9 Combine like terms: 0 + 9 = 9 4r = 9 Divide each side by '4'. r = 2.25 Simplifying r = 2.25

Solution

r = {0, 2.25}

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