6r^2-14r+15r-35=0

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Solution for 6r^2-14r+15r-35=0 equation:


Simplifying
6r2 + -14r + 15r + -35 = 0

Reorder the terms:
-35 + -14r + 15r + 6r2 = 0

Combine like terms: -14r + 15r = 1r
-35 + 1r + 6r2 = 0

Solving
-35 + 1r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -2r)(7 + -3r) = 0

Subproblem 1

Set the factor '(-5 + -2r)' equal to zero and attempt to solve: Simplifying -5 + -2r = 0 Solving -5 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2r = 0 + 5 -2r = 0 + 5 Combine like terms: 0 + 5 = 5 -2r = 5 Divide each side by '-2'. r = -2.5 Simplifying r = -2.5

Subproblem 2

Set the factor '(7 + -3r)' equal to zero and attempt to solve: Simplifying 7 + -3r = 0 Solving 7 + -3r = 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 + -3r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3r = 0 + -7 -3r = 0 + -7 Combine like terms: 0 + -7 = -7 -3r = -7 Divide each side by '-3'. r = 2.333333333 Simplifying r = 2.333333333

Solution

r = {-2.5, 2.333333333}

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