7p-(3p+4)=-2p(2p-1)+10

Solution for 7p-(3p+4)=-2p(2p-1)+10 equation:

Simplifying
7p + -1(3p + 4) = -2p(2p + -1) + 10

Reorder the terms:
7p + -1(4 + 3p) = -2p(2p + -1) + 10
7p + (4 * -1 + 3p * -1) = -2p(2p + -1) + 10
7p + (-4 + -3p) = -2p(2p + -1) + 10

Reorder the terms:
-4 + 7p + -3p = -2p(2p + -1) + 10

Combine like terms: 7p + -3p = 4p
-4 + 4p = -2p(2p + -1) + 10

Reorder the terms:
-4 + 4p = -2p(-1 + 2p) + 10
-4 + 4p = (-1 * -2p + 2p * -2p) + 10
-4 + 4p = (2p + -4p2) + 10

Reorder the terms:
-4 + 4p = 10 + 2p + -4p2

Solving
-4 + 4p = 10 + 2p + -4p2

Solving for variable 'p'.

Reorder the terms:
-4 + -10 + 4p + -2p + 4p2 = 10 + 2p + -4p2 + -10 + -2p + 4p2

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

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

Reorder the terms:
-14 + 2p + 4p2 = 10 + -10 + 2p + -2p + -4p2 + 4p2

Combine like terms: 10 + -10 = 0
-14 + 2p + 4p2 = 0 + 2p + -2p + -4p2 + 4p2
-14 + 2p + 4p2 = 2p + -2p + -4p2 + 4p2

Combine like terms: 2p + -2p = 0
-14 + 2p + 4p2 = 0 + -4p2 + 4p2
-14 + 2p + 4p2 = -4p2 + 4p2

Combine like terms: -4p2 + 4p2 = 0
-14 + 2p + 4p2 = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + p + 2p2)' equal to zero and attempt to solve:

Simplifying
-7 + p + 2p2 = 0

Solving
-7 + p + 2p2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-3.5 + 0.5p + p2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 0.5p + 3.5 + p2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 0.5p + p2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 0.5p + p2 = 0 + 3.5
0.5p + p2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
0.5p + p2 = 3.5

The p term is p.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5p + 0.25 + p2 = 3.5 + 0.25

Reorder the terms:
0.25 + 0.5p + p2 = 3.5 + 0.25

Combine like terms: 3.5 + 0.25 = 3.75
0.25 + 0.5p + p2 = 3.75

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(p + 0.5) equal to 1.936491673 and -1.936491673.

Subproblem 1
p + 0.5 = 1.936491673

Simplifying
p + 0.5 = 1.936491673

Reorder the terms:
0.5 + p = 1.936491673

Solving
0.5 + p = 1.936491673

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = 1.936491673 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = 1.936491673 + -0.5
p = 1.936491673 + -0.5

Combine like terms: 1.936491673 + -0.5 = 1.436491673
p = 1.436491673

Simplifying
p = 1.436491673

Subproblem 2
p + 0.5 = -1.936491673

Simplifying
p + 0.5 = -1.936491673

Reorder the terms:
0.5 + p = -1.936491673

Solving
0.5 + p = -1.936491673

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = -1.936491673 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = -1.936491673 + -0.5
p = -1.936491673 + -0.5

Combine like terms: -1.936491673 + -0.5 = -2.436491673
p = -2.436491673

Simplifying
p = -2.436491673

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.436491673, -2.436491673}
Solution
p = {1.436491673, -2.436491673}