6r^2-5r-4=7

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Solution for 6r^2-5r-4=7 equation:


Simplifying
6r2 + -5r + -4 = 7

Reorder the terms:
-4 + -5r + 6r2 = 7

Solving
-4 + -5r + 6r2 = 7

Solving for variable 'r'.

Reorder the terms:
-4 + -7 + -5r + 6r2 = 7 + -7

Combine like terms: -4 + -7 = -11
-11 + -5r + 6r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-11 + -5r + 6r2 = 0

Factor a trinomial.
(-1 + -1r)(11 + -6r) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(11 + -6r)' equal to zero and attempt to solve: Simplifying 11 + -6r = 0 Solving 11 + -6r = 0 Move all terms containing r to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -6r = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -6r = 0 + -11 -6r = 0 + -11 Combine like terms: 0 + -11 = -11 -6r = -11 Divide each side by '-6'. r = 1.833333333 Simplifying r = 1.833333333

Solution

r = {-1, 1.833333333}

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