2p(p-5)=7p-35

Solution for 2p(p-5)=7p-35 equation:

Simplifying
2p(p + -5) = 7p + -35

Reorder the terms:
2p(-5 + p) = 7p + -35
(-5 * 2p + p * 2p) = 7p + -35
(-10p + 2p2) = 7p + -35

Reorder the terms:
-10p + 2p2 = -35 + 7p

Solving
-10p + 2p2 = -35 + 7p

Solving for variable 'p'.

Reorder the terms:
35 + -10p + -7p + 2p2 = -35 + 7p + 35 + -7p

Combine like terms: -10p + -7p = -17p
35 + -17p + 2p2 = -35 + 7p + 35 + -7p

Reorder the terms:
35 + -17p + 2p2 = -35 + 35 + 7p + -7p

Combine like terms: -35 + 35 = 0
35 + -17p + 2p2 = 0 + 7p + -7p
35 + -17p + 2p2 = 7p + -7p

Combine like terms: 7p + -7p = 0
35 + -17p + 2p2 = 0

Factor a trinomial.
(7 + -2p)(5 + -1p) = 0

Subproblem 1
Set the factor '(7 + -2p)' equal to zero and attempt to solve:

Simplifying
7 + -2p = 0

Solving
7 + -2p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -2p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2p = 0 + -7
-2p = 0 + -7

Combine like terms: 0 + -7 = -7
-2p = -7

Divide each side by '-2'.
p = 3.5

Simplifying
p = 3.5
Subproblem 2
Set the factor '(5 + -1p)' equal to zero and attempt to solve:

Simplifying
5 + -1p = 0

Solving
5 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1p = 0 + -5
-1p = 0 + -5

Combine like terms: 0 + -5 = -5
-1p = -5

Divide each side by '-1'.
p = 5

Simplifying
p = 5
Solution
p = {3.5, 5}