4p(5p-6)=(2p+3)(2p-3)

Solution for 4p(5p-6)=(2p+3)(2p-3) equation:

Simplifying
4p(5p + -6) = (2p + 3)(2p + -3)

Reorder the terms:
4p(-6 + 5p) = (2p + 3)(2p + -3)
(-6 * 4p + 5p * 4p) = (2p + 3)(2p + -3)
(-24p + 20p2) = (2p + 3)(2p + -3)

Reorder the terms:
-24p + 20p2 = (3 + 2p)(2p + -3)

Reorder the terms:
-24p + 20p2 = (3 + 2p)(-3 + 2p)

Multiply (3 + 2p) * (-3 + 2p)
-24p + 20p2 = (3(-3 + 2p) + 2p * (-3 + 2p))
-24p + 20p2 = ((-3 * 3 + 2p * 3) + 2p * (-3 + 2p))
-24p + 20p2 = ((-9 + 6p) + 2p * (-3 + 2p))
-24p + 20p2 = (-9 + 6p + (-3 * 2p + 2p * 2p))
-24p + 20p2 = (-9 + 6p + (-6p + 4p2))

Combine like terms: 6p + -6p = 0
-24p + 20p2 = (-9 + 0 + 4p2)
-24p + 20p2 = (-9 + 4p2)

Solving
-24p + 20p2 = -9 + 4p2

Solving for variable 'p'.

Reorder the terms:
9 + -24p + 20p2 + -4p2 = -9 + 4p2 + 9 + -4p2

Combine like terms: 20p2 + -4p2 = 16p2
9 + -24p + 16p2 = -9 + 4p2 + 9 + -4p2

Reorder the terms:
9 + -24p + 16p2 = -9 + 9 + 4p2 + -4p2

Combine like terms: -9 + 9 = 0
9 + -24p + 16p2 = 0 + 4p2 + -4p2
9 + -24p + 16p2 = 4p2 + -4p2

Combine like terms: 4p2 + -4p2 = 0
9 + -24p + 16p2 = 0

Factor a trinomial.
(3 + -4p)(3 + -4p) = 0

Subproblem 1
Set the factor '(3 + -4p)' equal to zero and attempt to solve:

Simplifying
3 + -4p = 0

Solving
3 + -4p = 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 + -4p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4p = 0 + -3
-4p = 0 + -3

Combine like terms: 0 + -3 = -3
-4p = -3

Divide each side by '-4'.
p = 0.75

Simplifying
p = 0.75
Subproblem 2
Set the factor '(3 + -4p)' equal to zero and attempt to solve:

Simplifying
3 + -4p = 0

Solving
3 + -4p = 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 + -4p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4p = 0 + -3
-4p = 0 + -3

Combine like terms: 0 + -3 = -3
-4p = -3

Divide each side by '-4'.
p = 0.75

Simplifying
p = 0.75
Solution
p = {0.75, 0.75}