-(2-a-a2)+(3a2-5a+2)=120

Simplify each term.

Apply the distributive property.

-1⋅2–a–a2+3a2-5a+2=120

Simplify.

Multiply -1 by 2.

-2–a–a2+3a2-5a+2=120

Multiply –a.

Multiply -1 by -1.

-2+1a–a2+3a2-5a+2=120

Multiply a by 1.

-2+a–a2+3a2-5a+2=120

-2+a–a2+3a2-5a+2=120

Multiply –a2.

Multiply -1 by -1.

-2+a+1a2+3a2-5a+2=120

Multiply a2 by 1.

-2+a+a2+3a2-5a+2=120

-2+a+a2+3a2-5a+2=120

-2+a+a2+3a2-5a+2=120

-2+a+a2+3a2-5a+2=120

Simplify by adding terms.

Combine the opposite terms in -2+a+a2+3a2-5a+2.

Add -2 and 2.

a+a2+3a2-5a+0=120

Add a+a2+3a2-5a and 0.

a+a2+3a2-5a=120

a+a2+3a2-5a=120

Subtract 5a from a.

a2+3a2-4a=120

Add a2 and 3a2.

4a2-4a=120

4a2-4a=120

4a2-4a=120

Move 120 to the left side of the equation by subtracting it from both sides.

4a2-4a-120=0

Factor 4 out of 4a2-4a-120.

Factor 4 out of 4a2.

4(a2)-4a-120=0

Factor 4 out of -4a.

4(a2)+4(-a)-120=0

Factor 4 out of -120.

4(a2)+4(-a)+4(-30)=0

Factor 4 out of 4(a2)+4(-a).

4(a2-a)+4(-30)=0

Factor 4 out of 4(a2-a)+4(-30).

4(a2-a-30)=0

4(a2-a-30)=0

Factor.

Factor a2-a-30 using the AC method.

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 -30 and whose sum is -1.

-6,5

Write the factored form using these integers.

4((a-6)(a+5))=0

4((a-6)(a+5))=0

Remove unnecessary parentheses.

4(a-6)(a+5)=0

4(a-6)(a+5)=0

4(a-6)(a+5)=0

Divide each term in 4(a-6)(a+5)=0 by 4.

4(a-6)(a+5)4=04

Simplify 4(a-6)(a+5)4.

Cancel the common factor of 4.

Cancel the common factor.

4(a-6)(a+5)4=04

Divide (a-6)(a+5) by 1.

(a-6)(a+5)=04

(a-6)(a+5)=04

Expand (a-6)(a+5) using the FOIL Method.

Apply the distributive property.

a(a+5)-6(a+5)=04

Apply the distributive property.

a⋅a+a⋅5-6(a+5)=04

Apply the distributive property.

a⋅a+a⋅5-6a-6⋅5=04

a⋅a+a⋅5-6a-6⋅5=04

Simplify and combine like terms.

Simplify each term.

Multiply a by a.

a2+a⋅5-6a-6⋅5=04

Move 5 to the left of a.

a2+5⋅a-6a-6⋅5=04

Multiply -6 by 5.

a2+5a-6a-30=04

a2+5a-6a-30=04

Subtract 6a from 5a.

a2-a-30=04

a2-a-30=04

a2-a-30=04

Divide 0 by 4.

a2-a-30=0

a2-a-30=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 -30 and whose sum is -1.

-6,5

Write the factored form using these integers.

(a-6)(a+5)=0

(a-6)(a+5)=0

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

a-6=0

a+5=0

Set the first factor equal to 0.

a-6=0

Add 6 to both sides of the equation.

a=6

a=6

Set the next factor equal to 0.

a+5=0

Subtract 5 from both sides of the equation.

a=-5

a=-5

The final solution is all the values that make (a-6)(a+5)=0 true.

a=6,-5

Solve for a -(2-a-a^2)+(3a^2-5a+2)=120