4p^2=14p-6

Solution for 4p^2=14p-6 equation:

Simplifying
4p2 = 14p + -6

Reorder the terms:
4p2 = -6 + 14p

Solving
4p2 = -6 + 14p

Solving for variable 'p'.

Reorder the terms:
6 + -14p + 4p2 = -6 + 14p + 6 + -14p

Reorder the terms:
6 + -14p + 4p2 = -6 + 6 + 14p + -14p

Combine like terms: -6 + 6 = 0
6 + -14p + 4p2 = 0 + 14p + -14p
6 + -14p + 4p2 = 14p + -14p

Combine like terms: 14p + -14p = 0
6 + -14p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -7p + 2p2) = 0

Factor a trinomial.
2((1 + -2p)(3 + -1p)) = 0

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

Simplifying
1 + -2p = 0

Solving
1 + -2p = 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 + -2p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2p = 0 + -1
-2p = 0 + -1

Combine like terms: 0 + -1 = -1
-2p = -1

Divide each side by '-2'.
p = 0.5

Simplifying
p = 0.5
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 = {0.5, 3}