3x*(x+2)+((x-1)*(x-1))=x+1

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


Simplifying
3x(x + 2) + ((x + -1)(x + -1)) = x + 1

Reorder the terms:
3x(2 + x) + ((x + -1)(x + -1)) = x + 1
(2 * 3x + x * 3x) + ((x + -1)(x + -1)) = x + 1
(6x + 3x2) + ((x + -1)(x + -1)) = x + 1

Reorder the terms:
6x + 3x2 + ((-1 + x)(x + -1)) = x + 1

Reorder the terms:
6x + 3x2 + ((-1 + x)(-1 + x)) = x + 1

Multiply (-1 + x) * (-1 + x)
6x + 3x2 + ((-1(-1 + x) + x(-1 + x))) = x + 1
6x + 3x2 + (((-1 * -1 + x * -1) + x(-1 + x))) = x + 1
6x + 3x2 + (((1 + -1x) + x(-1 + x))) = x + 1
6x + 3x2 + ((1 + -1x + (-1 * x + x * x))) = x + 1
6x + 3x2 + ((1 + -1x + (-1x + x2))) = x + 1

Combine like terms: -1x + -1x = -2x
6x + 3x2 + ((1 + -2x + x2)) = x + 1
6x + 3x2 + (1 + -2x + x2) = x + 1

Remove parenthesis around (1 + -2x + x2)
6x + 3x2 + 1 + -2x + x2 = x + 1

Reorder the terms:
1 + 6x + -2x + 3x2 + x2 = x + 1

Combine like terms: 6x + -2x = 4x
1 + 4x + 3x2 + x2 = x + 1

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

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

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

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

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

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

Solving
4x + 4x2 = x

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + 4x) = 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 '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4x = 0 + -3

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

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

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Solution
x = {0, -0.75}

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