x^2+2x+1=4x^2-12x+9

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Solution for x^2+2x+1=4x^2-12x+9 equation: 


Simplifying
x2 + 2x + 1 = 4x2 + -12x + 9

Reorder the terms:
1 + 2x + x2 = 4x2 + -12x + 9

Reorder the terms:
1 + 2x + x2 = 9 + -12x + 4x2

Solving
1 + 2x + x2 = 9 + -12x + 4x2

Solving for variable 'x'.

Reorder the terms:
1 + -9 + 2x + 12x + x2 + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2

Combine like terms: 1 + -9 = -8
-8 + 2x + 12x + x2 + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2

Combine like terms: 2x + 12x = 14x
-8 + 14x + x2 + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2

Combine like terms: x2 + -4x2 = -3x2
-8 + 14x + -3x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2

Reorder the terms:
-8 + 14x + -3x2 = 9 + -9 + -12x + 12x + 4x2 + -4x2

Combine like terms: 9 + -9 = 0
-8 + 14x + -3x2 = 0 + -12x + 12x + 4x2 + -4x2
-8 + 14x + -3x2 = -12x + 12x + 4x2 + -4x2

Combine like terms: -12x + 12x = 0
-8 + 14x + -3x2 = 0 + 4x2 + -4x2
-8 + 14x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-8 + 14x + -3x2 = 0

Factor a trinomial.
(-4 + x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

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

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

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

Simplifying
x = 4

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {4, 0.6666666667}

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