12⋅(4t-7)=t+74

Move t+74 to the left side of the equation by subtracting it from both sides.

12⋅(4t-7)-t+74=0

Simplify each term.

Apply the distributive property.

12(4t)+12⋅-7-t+74=0

Cancel the common factor of 2.

Factor 2 out of 4t.

12(2(2t))+12⋅-7-t+74=0

Cancel the common factor.

12(2(2t))+12⋅-7-t+74=0

Rewrite the expression.

2t+12⋅-7-t+74=0

2t+12⋅-7-t+74=0

Combine 12 and -7.

2t+-72-t+74=0

Move the negative in front of the fraction.

2t-72-t+74=0

2t-72-t+74=0

To write 2t as a fraction with a common denominator, multiply by 44.

2t⋅44-t+74-72=0

Simplify terms.

Combine 2t and 44.

2t⋅44-t+74-72=0

Combine the numerators over the common denominator.

2t⋅4-(t+7)4-72=0

2t⋅4-(t+7)4-72=0

Simplify the numerator.

Multiply 4 by 2.

8t-(t+7)4-72=0

Apply the distributive property.

8t-t-1⋅74-72=0

Multiply -1 by 7.

8t-t-74-72=0

Subtract t from 8t.

7t-74-72=0

Factor 7 out of 7t-7.

Factor 7 out of 7t.

7(t)-74-72=0

Factor 7 out of -7.

7(t)+7(-1)4-72=0

Factor 7 out of 7(t)+7(-1).

7(t-1)4-72=0

7(t-1)4-72=0

7(t-1)4-72=0

To write -72 as a fraction with a common denominator, multiply by 22.

7(t-1)4-72⋅22=0

Write each expression with a common denominator of 4, by multiplying each by an appropriate factor of 1.

Multiply 72 and 22.

7(t-1)4-7⋅22⋅2=0

Multiply 2 by 2.

7(t-1)4-7⋅24=0

7(t-1)4-7⋅24=0

Combine the numerators over the common denominator.

7(t-1)-7⋅24=0

Simplify the numerator.

Factor 7 out of 7(t-1)-7⋅2.

Factor 7 out of -7⋅2.

7(t-1)+7(-1⋅2)4=0

Factor 7 out of 7(t-1)+7(-1⋅2).

7(t-1-1⋅2)4=0

7(t-1-1⋅2)4=0

Multiply -1 by 2.

7(t-1-2)4=0

Subtract 2 from -1.

7(t-3)4=0

7(t-3)4=0

7(t-3)4=0

Since this is the only denominator in the list, the result is the LCD: 4.

4

Multiply each term in 7(t-3)4=0 by 4.

7(t-3)4⋅4=0⋅4

Simplify 7(t-3)4⋅4.

Cancel the common factor of 4.

Cancel the common factor.

7(t-3)4⋅4=0⋅4

Rewrite the expression.

7(t-3)=0⋅4

7(t-3)=0⋅4

Apply the distributive property.

7t+7⋅-3=0⋅4

Multiply 7 by -3.

7t-21=0⋅4

7t-21=0⋅4

Multiply 0 by 4.

7t-21=0

7t-21=0

Add 21 to both sides of the equation.

7t=21

Divide each term in 7t=21 by 7.

7t7=217

Cancel the common factor of 7.

Cancel the common factor.

7t7=217

Divide t by 1.

t=217

t=217

Divide 21 by 7.

t=3

t=3

Solve for t 1/2*(4t-7)=(t+7)/4