P(x)+R(x)=(4x^2-1)+(6x^2+x+1)

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Solution for P(x)+R(x)=(4x^2-1)+(6x^2+x+1) equation: 


Simplifying
P(x) + R(x) = (4x2 + -1) + (6x2 + x + 1)

Multiply P * x
xP + R(x) = (4x2 + -1) + (6x2 + x + 1)

Multiply R * x
xP + xR = (4x2 + -1) + (6x2 + x + 1)

Reorder the terms:
xP + xR = (-1 + 4x2) + (6x2 + x + 1)

Remove parenthesis around (-1 + 4x2)
xP + xR = -1 + 4x2 + (6x2 + x + 1)

Reorder the terms:
xP + xR = -1 + 4x2 + (1 + x + 6x2)

Remove parenthesis around (1 + x + 6x2)
xP + xR = -1 + 4x2 + 1 + x + 6x2

Reorder the terms:
xP + xR = -1 + 1 + x + 4x2 + 6x2

Combine like terms: -1 + 1 = 0
xP + xR = 0 + x + 4x2 + 6x2
xP + xR = x + 4x2 + 6x2

Combine like terms: 4x2 + 6x2 = 10x2
xP + xR = x + 10x2

Solving
xP + xR = x + 10x2

Solving for variable 'x'.

Reorder the terms:
-1x + xP + xR + -10x2 = x + 10x2 + -1x + -10x2

Reorder the terms:
-1x + xP + xR + -10x2 = x + -1x + 10x2 + -10x2

Combine like terms: x + -1x = 0
-1x + xP + xR + -10x2 = 0 + 10x2 + -10x2
-1x + xP + xR + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-1x + xP + xR + -10x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + P + R + -10x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-1 + P + R + -10x)' equal to zero and attempt to solve:

Simplifying
-1 + P + R + -10x = 0

Solving
-1 + P + R + -10x = 0

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

Add '1' to each side of the equation.
-1 + P + R + 1 + -10x = 0 + 1

Reorder the terms:
-1 + 1 + P + R + -10x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + P + R + -10x = 0 + 1
P + R + -10x = 0 + 1

Combine like terms: 0 + 1 = 1
P + R + -10x = 1

Add '-1P' to each side of the equation.
P + R + -1P + -10x = 1 + -1P

Reorder the terms:
P + -1P + R + -10x = 1 + -1P

Combine like terms: P + -1P = 0
0 + R + -10x = 1 + -1P
R + -10x = 1 + -1P

Add '-1R' to each side of the equation.
R + -1R + -10x = 1 + -1P + -1R

Combine like terms: R + -1R = 0
0 + -10x = 1 + -1P + -1R
-10x = 1 + -1P + -1R

Divide each side by '-10'.
x = -0.1 + 0.1P + 0.1R

Simplifying
x = -0.1 + 0.1P + 0.1R
Solution
x = {0, -0.1 + 0.1P + 0.1R}

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