Solve for t 3/5t-1/10t=t-5/2

Math
35t-110t=t-52
Simplify 35t-110t.
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Simplify each term.
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Combine 35 and t.
3t5-110t=t-52
Combine t and 110.
3t5-t10=t-52
3t5-t10=t-52
To write 3t5 as a fraction with a common denominator, multiply by 22.
3t5⋅22-t10=t-52
Write each expression with a common denominator of 10, by multiplying each by an appropriate factor of 1.
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Multiply 3t5 and 22.
3t⋅25⋅2-t10=t-52
Multiply 5 by 2.
3t⋅210-t10=t-52
3t⋅210-t10=t-52
Combine the numerators over the common denominator.
3t⋅2-t10=t-52
Simplify the numerator.
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Factor t out of 3t⋅2-t.
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Factor t out of 3t⋅2.
t(3⋅2)-t10=t-52
Factor t out of -t.
t(3⋅2)+t⋅-110=t-52
Factor t out of t(3⋅2)+t⋅-1.
t(3⋅2-1)10=t-52
t(3⋅2-1)10=t-52
Multiply 3 by 2.
t(6-1)10=t-52
Subtract 1 from 6.
t⋅510=t-52
t⋅510=t-52
Cancel the common factor of 5 and 10.
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Factor 5 out of t⋅5.
5⋅t10=t-52
Cancel the common factors.
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Factor 5 out of 10.
5⋅t5⋅2=t-52
Cancel the common factor.
5⋅t5⋅2=t-52
Rewrite the expression.
t2=t-52
t2=t-52
t2=t-52
t2=t-52
Move all terms containing t to the left side of the equation.
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Subtract t from both sides of the equation.
t2-t=-52
To write -t as a fraction with a common denominator, multiply by 22.
t2-t⋅22=-52
Combine -t and 22.
t2+-t⋅22=-52
Combine the numerators over the common denominator.
t-t⋅22=-52
Simplify the numerator.
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Factor t out of t-t⋅2.
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Raise t to the power of 1.
t1-t⋅22=-52
Factor t out of t1.
t⋅1-t⋅22=-52
Factor t out of -t⋅2.
t⋅1+t(-1⋅2)2=-52
Factor t out of t⋅1+t(-1⋅2).
t(1-1⋅2)2=-52
t(1-1⋅2)2=-52
Multiply -1 by 2.
t(1-2)2=-52
Subtract 2 from 1.
t⋅-12=-52
t⋅-12=-52
Move -1 to the left of t.
-1⋅t2=-52
Move the negative in front of the fraction.
-t2=-52
-t2=-52
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
-t=-5
Multiply each term in -t=-5 by -1
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Multiply each term in -t=-5 by -1.
(-t)⋅-1=(-5)⋅-1
Multiply (-t)⋅-1.
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Multiply -1 by -1.
1t=(-5)⋅-1
Multiply t by 1.
t=(-5)⋅-1
t=(-5)⋅-1
Multiply -5 by -1.
t=5
t=5
Solve for t 3/5t-1/10t=t-5/2

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