# Solve for t -1/2*(t+9)+5 3/4*t=3/8t

-12⋅(t+9)+534⋅t=38t
Simplify -12⋅(t+9)+534⋅t.
Convert 534 to an improper fraction.
A mixed number is an addition of its whole and fractional parts.
-12⋅(t+9)+(5+34)⋅t=38t
To write 5 as a fraction with a common denominator, multiply by 44.
-12⋅(t+9)+(5⋅44+34)⋅t=38t
Combine 5 and 44.
-12⋅(t+9)+(5⋅44+34)⋅t=38t
Combine the numerators over the common denominator.
-12⋅(t+9)+5⋅4+34⋅t=38t
Simplify the numerator.
Multiply 5 by 4.
-12⋅(t+9)+20+34⋅t=38t
-12⋅(t+9)+234⋅t=38t
-12⋅(t+9)+234⋅t=38t
-12⋅(t+9)+234⋅t=38t
-12⋅(t+9)+234⋅t=38t
Simplify each term.
Apply the distributive property.
-12t-12⋅9+234⋅t=38t
Combine t and 12.
-t2-12⋅9+234⋅t=38t
Multiply -12⋅9.
Multiply 9 by -1.
-t2-9(12)+234⋅t=38t
Combine -9 and 12.
-t2+-92+234⋅t=38t
-t2+-92+234⋅t=38t
Move the negative in front of the fraction.
-t2-92+234⋅t=38t
Combine 234 and t.
-t2-92+23t4=38t
-t2-92+23t4=38t
To write -t2 as a fraction with a common denominator, multiply by 22.
-t2⋅22+23t4-92=38t
Write each expression with a common denominator of 4, by multiplying each by an appropriate factor of 1.
Multiply t2 and 22.
-t⋅22⋅2+23t4-92=38t
Multiply 2 by 2.
-t⋅24+23t4-92=38t
-t⋅24+23t4-92=38t
Combine the numerators over the common denominator.
-t⋅2+23t4-92=38t
Simplify each term.
Simplify the numerator.
Factor t out of -t⋅2+23t.
Factor t out of -t⋅2.
t(-1⋅2)+23t4-92=38t
Factor t out of 23t.
t(-1⋅2)+t⋅234-92=38t
Factor t out of t(-1⋅2)+t⋅23.
t(-1⋅2+23)4-92=38t
t(-1⋅2+23)4-92=38t
Multiply -1 by 2.
t(-2+23)4-92=38t
t⋅214-92=38t
t⋅214-92=38t
Move 21 to the left of t.
21t4-92=38t
21t4-92=38t
21t4-92=38t
Combine 38 and t.
21t4-92=3t8
Move 3t8 to the left side of the equation by subtracting it from both sides.
21t4-92-3t8=0
Simplify 21t4-92-3t8.
To write 21t4 as a fraction with a common denominator, multiply by 22.
21t4⋅22-3t8-92=0
Write each expression with a common denominator of 8, by multiplying each by an appropriate factor of 1.
Multiply 21t4 and 22.
21t⋅24⋅2-3t8-92=0
Multiply 4 by 2.
21t⋅28-3t8-92=0
21t⋅28-3t8-92=0
Combine the numerators over the common denominator.
21t⋅2-3t8-92=0
Simplify each term.
Simplify the numerator.
Factor 3t out of 21t⋅2-3t.
Factor 3t out of 21t⋅2.
3t(7⋅2)-3t8-92=0
Factor 3t out of -3t.
3t(7⋅2)+3t(-1)8-92=0
Factor 3t out of 3t(7⋅2)+3t(-1).
3t(7⋅2-1)8-92=0
3t(7⋅2-1)8-92=0
Multiply 7 by 2.
3t(14-1)8-92=0
Subtract 1 from 14.
3t⋅138-92=0
3t⋅138-92=0
Multiply 13 by 3.
39t8-92=0
39t8-92=0
39t8-92=0
Find the LCD of the terms in the equation.
To find the LCD of a set of numbers (39t8,-92), find the LCM of the denominators.
LCM(8,2)
Calculate the LCM of first two denominators in the list, 8 and 2.
Find the values of the numerical part of each term. Select the largest one, which in this case is 8. Multiply them together to get the current total. In this case, the current total is 16.
Current Total = 16
Check each value in the numerical part of each term against the current total. Since the current total is evenly divisible, return it. That is the least common denominator of the numerical part of the fraction.
8
8
8
Multiply each term by 8 and simplify.
Multiply each term in 39t8-92=0 by 8.
39t8⋅8-92⋅8=0⋅8
Simplify each term.
Cancel the common factor of 8.
Cancel the common factor.
39t8⋅8-92⋅8=0⋅8
Rewrite the expression.
39t-92⋅8=0⋅8
39t-92⋅8=0⋅8
Cancel the common factor of 2.
Move the leading negative in -92 into the numerator.
39t+-92⋅8=0⋅8
Factor 2 out of 8.
39t+-92⋅(2(4))=0⋅8
Cancel the common factor.
39t+-92⋅(2⋅4)=0⋅8
Rewrite the expression.
39t-9⋅4=0⋅8
39t-9⋅4=0⋅8
Multiply -9 by 4.
39t-36=0⋅8
39t-36=0⋅8
Multiply 0 by 8.
39t-36=0
39t-36=0
Add 36 to both sides of the equation.
39t=36
Divide each term by 39 and simplify.
Divide each term in 39t=36 by 39.
39t39=3639
Cancel the common factor of 39.
Cancel the common factor.
39t39=3639
Divide t by 1.
t=3639
t=3639
Cancel the common factor of 36 and 39.
Factor 3 out of 36.
t=3(12)39
Cancel the common factors.
Factor 3 out of 39.
t=3⋅123⋅13
Cancel the common factor.
t=3⋅123⋅13
Rewrite the expression.
t=1213
t=1213
t=1213
t=1213
The result can be shown in multiple forms.
Exact Form:
t=1213
Decimal Form:
t=0.923076‾
Solve for t -1/2*(t+9)+5 3/4*t=3/8t

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