7r^2-20=8-45r

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Solution for 7r^2-20=8-45r equation: 


Simplifying
7r2 + -20 = 8 + -45r

Reorder the terms:
-20 + 7r2 = 8 + -45r

Solving
-20 + 7r2 = 8 + -45r

Solving for variable 'r'.

Reorder the terms:
-20 + -8 + 45r + 7r2 = 8 + -45r + -8 + 45r

Combine like terms: -20 + -8 = -28
-28 + 45r + 7r2 = 8 + -45r + -8 + 45r

Reorder the terms:
-28 + 45r + 7r2 = 8 + -8 + -45r + 45r

Combine like terms: 8 + -8 = 0
-28 + 45r + 7r2 = 0 + -45r + 45r
-28 + 45r + 7r2 = -45r + 45r

Combine like terms: -45r + 45r = 0
-28 + 45r + 7r2 = 0

Factor a trinomial.
(-7 + -1r)(4 + -7r) = 0


Subproblem 1
Set the factor '(-7 + -1r)' equal to zero and attempt to solve:

Simplifying
-7 + -1r = 0

Solving
-7 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -1r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1r = 0 + 7
-1r = 0 + 7

Combine like terms: 0 + 7 = 7
-1r = 7

Divide each side by '-1'.
r = -7

Simplifying
r = -7

Subproblem 2
Set the factor '(4 + -7r)' equal to zero and attempt to solve:

Simplifying
4 + -7r = 0

Solving
4 + -7r = 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 + -7r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7r = 0 + -4
-7r = 0 + -4

Combine like terms: 0 + -4 = -4
-7r = -4

Divide each side by '-7'.
r = 0.5714285714

Simplifying
r = 0.5714285714
Solution
r = {-7, 0.5714285714}

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