-x^2+4x+1=4x^2+1-3x(x+1)

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Solution for -x^2+4x+1=4x^2+1-3x(x+1) equation: 


Simplifying
-1x2 + 4x + 1 = 4x2 + 1 + -3x(x + 1)

Reorder the terms:
1 + 4x + -1x2 = 4x2 + 1 + -3x(x + 1)

Reorder the terms:
1 + 4x + -1x2 = 4x2 + 1 + -3x(1 + x)
1 + 4x + -1x2 = 4x2 + 1 + (1 * -3x + x * -3x)
1 + 4x + -1x2 = 4x2 + 1 + (-3x + -3x2)

Reorder the terms:
1 + 4x + -1x2 = 1 + -3x + 4x2 + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
1 + 4x + -1x2 = 1 + -3x + 1x2

Add '-1' to each side of the equation.
1 + 4x + -1 + -1x2 = 1 + -3x + -1 + 1x2

Reorder the terms:
1 + -1 + 4x + -1x2 = 1 + -3x + -1 + 1x2

Combine like terms: 1 + -1 = 0
0 + 4x + -1x2 = 1 + -3x + -1 + 1x2
4x + -1x2 = 1 + -3x + -1 + 1x2

Reorder the terms:
4x + -1x2 = 1 + -1 + -3x + 1x2

Combine like terms: 1 + -1 = 0
4x + -1x2 = 0 + -3x + 1x2
4x + -1x2 = -3x + 1x2

Solving
4x + -1x2 = -3x + 1x2

Solving for variable 'x'.

Reorder the terms:
4x + 3x + -1x2 + -1x2 = -3x + 1x2 + 3x + -1x2

Combine like terms: 4x + 3x = 7x
7x + -1x2 + -1x2 = -3x + 1x2 + 3x + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
7x + -2x2 = -3x + 1x2 + 3x + -1x2

Reorder the terms:
7x + -2x2 = -3x + 3x + 1x2 + -1x2

Combine like terms: -3x + 3x = 0
7x + -2x2 = 0 + 1x2 + -1x2
7x + -2x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
7x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + -2x) = 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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0, 3.5}

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