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

-(2-a-a2)+(3a2-5a+2)=120
Simplify -(2-a-a2)+3a2-5a+2.
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
Combine the opposite terms in -2+a+a2+3a2-5a+2.
a+a2+3a2-5a+0=120
a+a2+3a2-5a=120
a+a2+3a2-5a=120
Subtract 5a from a.
a2+3a2-4a=120
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 the left side of the equation.
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 by 4 and simplify.
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
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.
(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 and solve.
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 and solve.
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

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