2p2=6p-20

Subtract 6p from both sides of the equation.

2p2-6p=-20

Move 20 to the left side of the equation by adding it to both sides.

2p2-6p+20=0

Factor 2 out of 2p2.

2(p2)-6p+20=0

Factor 2 out of -6p.

2(p2)+2(-3p)+20=0

Factor 2 out of 20.

2p2+2(-3p)+2⋅10=0

Factor 2 out of 2p2+2(-3p).

2(p2-3p)+2⋅10=0

Factor 2 out of 2(p2-3p)+2⋅10.

2(p2-3p+10)=0

2(p2-3p+10)=0

Divide each term in 2(p2-3p+10)=0 by 2.

2(p2-3p+10)2=02

Cancel the common factor of 2.

Cancel the common factor.

2(p2-3p+10)2=02

Divide p2-3p+10 by 1.

p2-3p+10=02

p2-3p+10=02

Divide 0 by 2.

p2-3p+10=0

p2-3p+10=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=-3, and c=10 into the quadratic formula and solve for p.

3±(-3)2-4⋅(1⋅10)2⋅1

Simplify the numerator.

Raise -3 to the power of 2.

p=3±9-4⋅(1⋅10)2⋅1

Multiply 10 by 1.

p=3±9-4⋅102⋅1

Multiply -4 by 10.

p=3±9-402⋅1

Subtract 40 from 9.

p=3±-312⋅1

Rewrite -31 as -1(31).

p=3±-1⋅312⋅1

Rewrite -1(31) as -1⋅31.

p=3±-1⋅312⋅1

Rewrite -1 as i.

p=3±i312⋅1

p=3±i312⋅1

Multiply 2 by 1.

p=3±i312

p=3±i312

The final answer is the combination of both solutions.

p=3+i312,3-i312

Solve for p 2p^2=6p-20