(2p-5)(3p+4)=5p-2

Solution for (2p-5)(3p+4)=5p-2 equation:

Simplifying
(2p + -5)(3p + 4) = 5p + -2

Reorder the terms:
(-5 + 2p)(3p + 4) = 5p + -2

Reorder the terms:
(-5 + 2p)(4 + 3p) = 5p + -2

Multiply (-5 + 2p) * (4 + 3p)
(-5(4 + 3p) + 2p * (4 + 3p)) = 5p + -2
((4 * -5 + 3p * -5) + 2p * (4 + 3p)) = 5p + -2
((-20 + -15p) + 2p * (4 + 3p)) = 5p + -2
(-20 + -15p + (4 * 2p + 3p * 2p)) = 5p + -2
(-20 + -15p + (8p + 6p2)) = 5p + -2

Combine like terms: -15p + 8p = -7p
(-20 + -7p + 6p2) = 5p + -2

Reorder the terms:
-20 + -7p + 6p2 = -2 + 5p

Solving
-20 + -7p + 6p2 = -2 + 5p

Solving for variable 'p'.

Reorder the terms:
-20 + 2 + -7p + -5p + 6p2 = -2 + 5p + 2 + -5p

Combine like terms: -20 + 2 = -18
-18 + -7p + -5p + 6p2 = -2 + 5p + 2 + -5p

Combine like terms: -7p + -5p = -12p
-18 + -12p + 6p2 = -2 + 5p + 2 + -5p

Reorder the terms:
-18 + -12p + 6p2 = -2 + 2 + 5p + -5p

Combine like terms: -2 + 2 = 0
-18 + -12p + 6p2 = 0 + 5p + -5p
-18 + -12p + 6p2 = 5p + -5p

Combine like terms: 5p + -5p = 0
-18 + -12p + 6p2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + -2p + p2) = 0

Factor a trinomial.
6((-1 + -1p)(3 + -1p)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -1p)' equal to zero and attempt to solve:

Simplifying
-1 + -1p = 0

Solving
-1 + -1p = 0

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

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

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

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

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

Simplifying
p = -1
Subproblem 2
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-1, 3}