# Solve for a (a+1)(2a-3)=30 (a+1)(2a-3)=30
Simplify (a+1)(2a-3).
Expand (a+1)(2a-3) using the FOIL Method.
Apply the distributive property.
a(2a-3)+1(2a-3)=30
Apply the distributive property.
a(2a)+a⋅-3+1(2a-3)=30
Apply the distributive property.
a(2a)+a⋅-3+1(2a)+1⋅-3=30
a(2a)+a⋅-3+1(2a)+1⋅-3=30
Simplify and combine like terms.
Simplify each term.
Rewrite using the commutative property of multiplication.
2a⋅a+a⋅-3+1(2a)+1⋅-3=30
Multiply a by a by adding the exponents.
Move a.
2(a⋅a)+a⋅-3+1(2a)+1⋅-3=30
Multiply a by a.
2a2+a⋅-3+1(2a)+1⋅-3=30
2a2+a⋅-3+1(2a)+1⋅-3=30
Move -3 to the left of a.
2a2-3⋅a+1(2a)+1⋅-3=30
Multiply 2a by 1.
2a2-3a+2a+1⋅-3=30
Multiply -3 by 1.
2a2-3a+2a-3=30
2a2-3a+2a-3=30
Add -3a and 2a.
2a2-a-3=30
2a2-a-3=30
2a2-a-3=30
Move all terms to the left side of the equation and simplify.
Move 30 to the left side of the equation by subtracting it from both sides.
2a2-a-3-30=0
Subtract 30 from -3.
2a2-a-33=0
2a2-a-33=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=2, b=-1, and c=-33 into the quadratic formula and solve for a.
1±(-1)2-4⋅(2⋅-33)2⋅2
Simplify.
Simplify the numerator.
Raise -1 to the power of 2.
a=1±1-4⋅(2⋅-33)2⋅2
Multiply 2 by -33.
a=1±1-4⋅-662⋅2
Multiply -4 by -66.
a=1±1+2642⋅2
Add 1 and 264.
a=1±2652⋅2
a=1±2652⋅2
Multiply 2 by 2.
a=1±2654
a=1±2654
The final answer is the combination of both solutions.
a=1+2654,1-2654
The result can be shown in multiple forms.
Exact Form:
a=1+2654,1-2654
Decimal Form:
a=4.31970514…,-3.81970514…
Solve for a (a+1)(2a-3)=30

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