6r^2+5r=2(r^2+2)-4(5-r^2)+1

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Solution for 6r^2+5r=2(r^2+2)-4(5-r^2)+1 equation: 


Simplifying
6r2 + 5r = 2(r2 + 2) + -4(5 + -1r2) + 1

Reorder the terms:
5r + 6r2 = 2(r2 + 2) + -4(5 + -1r2) + 1

Reorder the terms:
5r + 6r2 = 2(2 + r2) + -4(5 + -1r2) + 1
5r + 6r2 = (2 * 2 + r2 * 2) + -4(5 + -1r2) + 1
5r + 6r2 = (4 + 2r2) + -4(5 + -1r2) + 1
5r + 6r2 = 4 + 2r2 + (5 * -4 + -1r2 * -4) + 1
5r + 6r2 = 4 + 2r2 + (-20 + 4r2) + 1

Reorder the terms:
5r + 6r2 = 4 + -20 + 1 + 2r2 + 4r2

Combine like terms: 4 + -20 = -16
5r + 6r2 = -16 + 1 + 2r2 + 4r2

Combine like terms: -16 + 1 = -15
5r + 6r2 = -15 + 2r2 + 4r2

Combine like terms: 2r2 + 4r2 = 6r2
5r + 6r2 = -15 + 6r2

Add '-6r2' to each side of the equation.
5r + 6r2 + -6r2 = -15 + 6r2 + -6r2

Combine like terms: 6r2 + -6r2 = 0
5r + 0 = -15 + 6r2 + -6r2
5r = -15 + 6r2 + -6r2

Combine like terms: 6r2 + -6r2 = 0
5r = -15 + 0
5r = -15

Solving
5r = -15

Solving for variable 'r'.

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

Divide each side by '5'.
r = -3

Simplifying
r = -3

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