43⋅(t+1)-16⋅(4t-3)=2

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

Add 8 and 3.

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

Subtract 11 from both sides of the equation.

4t=12-11

Subtract 11 from 12.

4t=1

4t=1

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