10r(r)-21r=-4r+6

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Solution for 10r(r)-21r=-4r+6 equation:


Simplifying
10r(r) + -21r = -4r + 6

Multiply r * r
10r2 + -21r = -4r + 6

Reorder the terms:
-21r + 10r2 = -4r + 6

Reorder the terms:
-21r + 10r2 = 6 + -4r

Solving
-21r + 10r2 = 6 + -4r

Solving for variable 'r'.

Reorder the terms:
-6 + -21r + 4r + 10r2 = 6 + -4r + -6 + 4r

Combine like terms: -21r + 4r = -17r
-6 + -17r + 10r2 = 6 + -4r + -6 + 4r

Reorder the terms:
-6 + -17r + 10r2 = 6 + -6 + -4r + 4r

Combine like terms: 6 + -6 = 0
-6 + -17r + 10r2 = 0 + -4r + 4r
-6 + -17r + 10r2 = -4r + 4r

Combine like terms: -4r + 4r = 0
-6 + -17r + 10r2 = 0

Factor a trinomial.
(-3 + -10r)(2 + -1r) = 0

Subproblem 1

Set the factor '(-3 + -10r)' equal to zero and attempt to solve: Simplifying -3 + -10r = 0 Solving -3 + -10r = 0 Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -10r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -10r = 0 + 3 -10r = 0 + 3 Combine like terms: 0 + 3 = 3 -10r = 3 Divide each side by '-10'. r = -0.3 Simplifying r = -0.3

Subproblem 2

Set the factor '(2 + -1r)' equal to zero and attempt to solve: Simplifying 2 + -1r = 0 Solving 2 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r = 0 + -2 -1r = 0 + -2 Combine like terms: 0 + -2 = -2 -1r = -2 Divide each side by '-1'. r = 2 Simplifying r = 2

Solution

r = {-0.3, 2}

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