14p^2+p-2=4p^2

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

Simplifying
14p2 + p + -2 = 4p2

Reorder the terms:
-2 + p + 14p2 = 4p2

Solving
-2 + p + 14p2 = 4p2

Solving for variable 'p'.

Combine like terms: 14p2 + -4p2 = 10p2
-2 + p + 10p2 = 4p2 + -4p2

Combine like terms: 4p2 + -4p2 = 0
-2 + p + 10p2 = 0

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

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 '(2 + -5p)' equal to zero and attempt to solve:

Simplifying
2 + -5p = 0

Solving
2 + -5p = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5p = 0 + -2
-5p = 0 + -2

Combine like terms: 0 + -2 = -2
-5p = -2

Divide each side by '-5'.
p = 0.4

Simplifying
p = 0.4
Solution
p = {-0.5, 0.4}