Solve for r -2r+1/3-5/2r=-25/6

Math
-2r+13-52r=-256
Simplify -2r+13-52r.
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Simplify each term.
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Combine r and 52.
-2r+13-r⋅52=-256
Move 5 to the left of r.
-2r+13-5r2=-256
-2r+13-5r2=-256
To write -2r as a fraction with a common denominator, multiply by 22.
-2r⋅22-5r2+13=-256
Simplify terms.
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Combine -2r and 22.
-2r⋅22-5r2+13=-256
Combine the numerators over the common denominator.
-2r⋅2-5r2+13=-256
-2r⋅2-5r2+13=-256
Simplify each term.
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Simplify the numerator.
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Factor r out of -2r⋅2-5r.
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Factor r out of -2r⋅2.
r(-2⋅2)-5r2+13=-256
Factor r out of -5r.
r(-2⋅2)+r⋅-52+13=-256
Factor r out of r(-2⋅2)+r⋅-5.
r(-2⋅2-5)2+13=-256
r(-2⋅2-5)2+13=-256
Multiply -2 by 2.
r(-4-5)2+13=-256
Subtract 5 from -4.
r⋅-92+13=-256
r⋅-92+13=-256
Move -9 to the left of r.
-9⋅r2+13=-256
Move the negative in front of the fraction.
-9r2+13=-256
-9r2+13=-256
-9r2+13=-256
Move all terms not containing r to the right side of the equation.
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Subtract 13 from both sides of the equation.
-9r2=-256-13
To write -13 as a fraction with a common denominator, multiply by 22.
-9r2=-256-13⋅22
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
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Multiply 13 and 22.
-9r2=-256-23⋅2
Multiply 3 by 2.
-9r2=-256-26
-9r2=-256-26
Combine the numerators over the common denominator.
-9r2=-25-26
Subtract 2 from -25.
-9r2=-276
Cancel the common factor of -27 and 6.
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Factor 3 out of -27.
-9r2=3(-9)6
Cancel the common factors.
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Factor 3 out of 6.
-9r2=3⋅-93⋅2
Cancel the common factor.
-9r2=3⋅-93⋅2
Rewrite the expression.
-9r2=-92
-9r2=-92
-9r2=-92
Move the negative in front of the fraction.
-9r2=-92
-9r2=-92
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
-9r=-9
Divide each term by -9 and simplify.
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Divide each term in -9r=-9 by -9.
-9r-9=-9-9
Cancel the common factor of -9.
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Cancel the common factor.
-9r-9=-9-9
Divide r by 1.
r=-9-9
r=-9-9
Divide -9 by -9.
r=1
r=1
Solve for r -2r+1/3-5/2r=-25/6

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