# Solve for t 4/3*(t+1)-1/6*(4t-3)=2 43⋅(t+1)-16⋅(4t-3)=2
Simplify 43⋅(t+1)-16⋅(4t-3).
Simplify each term.
Apply the distributive property.
43t+43⋅1-16⋅(4t-3)=2
Combine 43 and t.
4t3+43⋅1-16⋅(4t-3)=2
Multiply 43 by 1.
4t3+43-16⋅(4t-3)=2
Apply the distributive property.
4t3+43-16(4t)-16⋅-3=2
Cancel the common factor of 2.
Move the leading negative in -16 into the numerator.
4t3+43+-16(4t)-16⋅-3=2
Factor 2 out of 6.
4t3+43+-12(3)(4t)-16⋅-3=2
Factor 2 out of 4t.
4t3+43+-12(3)(2(2t))-16⋅-3=2
Cancel the common factor.
4t3+43+-12⋅3(2(2t))-16⋅-3=2
Rewrite the expression.
4t3+43+-13(2t)-16⋅-3=2
4t3+43+-13(2t)-16⋅-3=2
Combine 2 and -13.
4t3+43+2⋅-13t-16⋅-3=2
Multiply 2 by -1.
4t3+43+-23t-16⋅-3=2
Combine -23 and t.
4t3+43+-2t3-16⋅-3=2
Cancel the common factor of 3.
Move the leading negative in -16 into the numerator.
4t3+43+-2t3+-16⋅-3=2
Factor 3 out of 6.
4t3+43+-2t3+-13(2)⋅-3=2
Factor 3 out of -3.
4t3+43+-2t3+-13⋅2⋅(3⋅-1)=2
Cancel the common factor.
4t3+43+-2t3+-13⋅2⋅(3⋅-1)=2
Rewrite the expression.
4t3+43+-2t3+-12⋅-1=2
4t3+43+-2t3+-12⋅-1=2
Combine -12 and -1.
4t3+43+-2t3+–12=2
Multiply -1 by -1.
4t3+43+-2t3+12=2
Move the negative in front of the fraction.
4t3+43-2t3+12=2
4t3+43-2t3+12=2
Simplify terms.
Combine fractions with similar denominators.
4t+4-2t3+12=2
Subtract 2t from 4t.
2t+43+12=2
Factor 2 out of 2t+4.
Factor 2 out of 2t.
2(t)+43+12=2
Factor 2 out of 4.
2t+2⋅23+12=2
Factor 2 out of 2t+2⋅2.
2(t+2)3+12=2
2(t+2)3+12=2
2(t+2)3+12=2
To write 2(t+2)3 as a fraction with a common denominator, multiply by 22.
2(t+2)3⋅22+12=2
To write 12 as a fraction with a common denominator, multiply by 33.
2(t+2)3⋅22+12⋅33=2
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
Multiply 2(t+2)3 and 22.
2(t+2)⋅23⋅2+12⋅33=2
Multiply 3 by 2.
2(t+2)⋅26+12⋅33=2
Multiply 12 and 33.
2(t+2)⋅26+32⋅3=2
Multiply 2 by 3.
2(t+2)⋅26+36=2
2(t+2)⋅26+36=2
Combine the numerators over the common denominator.
2(t+2)⋅2+36=2
Simplify the numerator.
Apply the distributive property.
(2t+2⋅2)⋅2+36=2
Multiply 2 by 2.
(2t+4)⋅2+36=2
Apply the distributive property.
2t⋅2+4⋅2+36=2
Multiply 2 by 2.
4t+4⋅2+36=2
Multiply 4 by 2.
4t+8+36=2
4t+116=2
4t+116=2
4t+116=2
Multiply both sides of the equation by 6.
4t+11=2⋅(6)
Remove parentheses.
4t+11=2⋅(6)
Multiply 2 by 6.
4t+11=12
Move all terms not containing t to the right side of the equation.
Subtract 11 from both sides of the equation.
4t=12-11
Subtract 11 from 12.
4t=1
4t=1
Divide each term by 4 and simplify.
Divide each term in 4t=1 by 4.
4t4=14
Cancel the common factor of 4.
Cancel the common factor.
4t4=14
Divide t by 1.
t=14
t=14
t=14
The result can be shown in multiple forms.
Exact Form:
t=14
Decimal Form:
t=0.25
Solve for t 4/3*(t+1)-1/6*(4t-3)=2

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