43r^2+35r-32=-8-6r^2

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Solution for 43r^2+35r-32=-8-6r^2 equation: 


Simplifying
43r2 + 35r + -32 = -8 + -6r2

Reorder the terms:
-32 + 35r + 43r2 = -8 + -6r2

Solving
-32 + 35r + 43r2 = -8 + -6r2

Solving for variable 'r'.

Reorder the terms:
-32 + 8 + 35r + 43r2 + 6r2 = -8 + -6r2 + 8 + 6r2

Combine like terms: -32 + 8 = -24
-24 + 35r + 43r2 + 6r2 = -8 + -6r2 + 8 + 6r2

Combine like terms: 43r2 + 6r2 = 49r2
-24 + 35r + 49r2 = -8 + -6r2 + 8 + 6r2

Reorder the terms:
-24 + 35r + 49r2 = -8 + 8 + -6r2 + 6r2

Combine like terms: -8 + 8 = 0
-24 + 35r + 49r2 = 0 + -6r2 + 6r2
-24 + 35r + 49r2 = -6r2 + 6r2

Combine like terms: -6r2 + 6r2 = 0
-24 + 35r + 49r2 = 0

Factor a trinomial.
(-8 + -7r)(3 + -7r) = 0


Subproblem 1
Set the factor '(-8 + -7r)' equal to zero and attempt to solve:

Simplifying
-8 + -7r = 0

Solving
-8 + -7r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7r = 0 + 8
-7r = 0 + 8

Combine like terms: 0 + 8 = 8
-7r = 8

Divide each side by '-7'.
r = -1.142857143

Simplifying
r = -1.142857143

Subproblem 2
Set the factor '(3 + -7r)' equal to zero and attempt to solve:

Simplifying
3 + -7r = 0

Solving
3 + -7r = 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 + -7r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7r = 0 + -3
-7r = 0 + -3

Combine like terms: 0 + -3 = -3
-7r = -3

Divide each side by '-7'.
r = 0.4285714286

Simplifying
r = 0.4285714286
Solution
r = {-1.142857143, 0.4285714286}

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