66=t2-t2

Rewrite the equation as t2-t2=66.

t2-t2=66

Multiply both sides of the equation by 2.

2⋅t2-t2=2⋅66

Simplify 2⋅t2-t2.

Simplify terms.

Factor t out of t2-t.

Factor t out of t2.

2⋅t⋅t-t2=2⋅66

Factor t out of -t.

2⋅t⋅t+t⋅-12=2⋅66

Factor t out of t⋅t+t⋅-1.

2⋅t(t-1)2=2⋅66

2⋅t(t-1)2=2⋅66

Cancel the common factor of 2.

Cancel the common factor.

2⋅t(t-1)2=2⋅66

Rewrite the expression.

t(t-1)=2⋅66

t(t-1)=2⋅66

Apply the distributive property.

t⋅t+t⋅-1=2⋅66

Simplify the expression.

Multiply t by t.

t2+t⋅-1=2⋅66

Move -1 to the left of t.

t2-1⋅t=2⋅66

t2-1⋅t=2⋅66

t2-1⋅t=2⋅66

Rewrite -1t as -t.

t2-t=2⋅66

t2-t=2⋅66

Multiply 2 by 66.

t2-t=132

t2-t=132

Move 132 to the left side of the equation by subtracting it from both sides.

t2-t-132=0

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -132 and whose sum is -1.

-12,11

Write the factored form using these integers.

(t-12)(t+11)=0

(t-12)(t+11)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

t-12=0

t+11=0

Set the first factor equal to 0.

t-12=0

Add 12 to both sides of the equation.

t=12

t=12

Set the next factor equal to 0.

t+11=0

Subtract 11 from both sides of the equation.

t=-11

t=-11

The final solution is all the values that make (t-12)(t+11)=0 true.

t=12,-11

Solve for t 66=(t^2-t)/2