4p^2=-7p-3

Solution for 4p^2=-7p-3 equation:

Simplifying
4p2 = -7p + -3

Reorder the terms:
4p2 = -3 + -7p

Solving
4p2 = -3 + -7p

Solving for variable 'p'.

Reorder the terms:
3 + 7p + 4p2 = -3 + -7p + 3 + 7p

Reorder the terms:
3 + 7p + 4p2 = -3 + 3 + -7p + 7p

Combine like terms: -3 + 3 = 0
3 + 7p + 4p2 = 0 + -7p + 7p
3 + 7p + 4p2 = -7p + 7p

Combine like terms: -7p + 7p = 0
3 + 7p + 4p2 = 0

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

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

Simplifying
1 + p = 0

Solving
1 + p = 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 + p = 0 + -1

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

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

Simplifying
p = -1
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 = {-1, -0.75}