(2x+1)(2x+1)-(x+13)=3x^2-2x+2

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Solution for (2x+1)(2x+1)-(x+13)=3x^2-2x+2 equation: 


Simplifying
(2x + 1)(2x + 1) + -1(x + 13) = 3x2 + -2x + 2

Reorder the terms:
(1 + 2x)(2x + 1) + -1(x + 13) = 3x2 + -2x + 2

Reorder the terms:
(1 + 2x)(1 + 2x) + -1(x + 13) = 3x2 + -2x + 2

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) + -1(x + 13) = 3x2 + -2x + 2
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) + -1(x + 13) = 3x2 + -2x + 2
((1 + 2x) + 2x * (1 + 2x)) + -1(x + 13) = 3x2 + -2x + 2
(1 + 2x + (1 * 2x + 2x * 2x)) + -1(x + 13) = 3x2 + -2x + 2
(1 + 2x + (2x + 4x2)) + -1(x + 13) = 3x2 + -2x + 2

Combine like terms: 2x + 2x = 4x
(1 + 4x + 4x2) + -1(x + 13) = 3x2 + -2x + 2

Reorder the terms:
1 + 4x + 4x2 + -1(13 + x) = 3x2 + -2x + 2
1 + 4x + 4x2 + (13 * -1 + x * -1) = 3x2 + -2x + 2
1 + 4x + 4x2 + (-13 + -1x) = 3x2 + -2x + 2

Reorder the terms:
1 + -13 + 4x + -1x + 4x2 = 3x2 + -2x + 2

Combine like terms: 1 + -13 = -12
-12 + 4x + -1x + 4x2 = 3x2 + -2x + 2

Combine like terms: 4x + -1x = 3x
-12 + 3x + 4x2 = 3x2 + -2x + 2

Reorder the terms:
-12 + 3x + 4x2 = 2 + -2x + 3x2

Solving
-12 + 3x + 4x2 = 2 + -2x + 3x2

Solving for variable 'x'.

Reorder the terms:
-12 + -2 + 3x + 2x + 4x2 + -3x2 = 2 + -2x + 3x2 + -2 + 2x + -3x2

Combine like terms: -12 + -2 = -14
-14 + 3x + 2x + 4x2 + -3x2 = 2 + -2x + 3x2 + -2 + 2x + -3x2

Combine like terms: 3x + 2x = 5x
-14 + 5x + 4x2 + -3x2 = 2 + -2x + 3x2 + -2 + 2x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-14 + 5x + 1x2 = 2 + -2x + 3x2 + -2 + 2x + -3x2

Reorder the terms:
-14 + 5x + 1x2 = 2 + -2 + -2x + 2x + 3x2 + -3x2

Combine like terms: 2 + -2 = 0
-14 + 5x + 1x2 = 0 + -2x + 2x + 3x2 + -3x2
-14 + 5x + 1x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
-14 + 5x + 1x2 = 0 + 3x2 + -3x2
-14 + 5x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-14 + 5x + 1x2 = 0

Factor a trinomial.
(-7 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

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

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

Divide each side by '-1'.
x = -7

Simplifying
x = -7

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-7, 2}

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