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

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


Simplifying
x2 + 4x + 4 = (x + 2)(3x + -4)

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

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

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

Multiply (2 + x) * (-4 + 3x)
4 + 4x + x2 = (2(-4 + 3x) + x(-4 + 3x))
4 + 4x + x2 = ((-4 * 2 + 3x * 2) + x(-4 + 3x))
4 + 4x + x2 = ((-8 + 6x) + x(-4 + 3x))
4 + 4x + x2 = (-8 + 6x + (-4 * x + 3x * x))
4 + 4x + x2 = (-8 + 6x + (-4x + 3x2))

Combine like terms: 6x + -4x = 2x
4 + 4x + x2 = (-8 + 2x + 3x2)

Solving
4 + 4x + x2 = -8 + 2x + 3x2

Solving for variable 'x'.

Reorder the terms:
4 + 8 + 4x + -2x + x2 + -3x2 = -8 + 2x + 3x2 + 8 + -2x + -3x2

Combine like terms: 4 + 8 = 12
12 + 4x + -2x + x2 + -3x2 = -8 + 2x + 3x2 + 8 + -2x + -3x2

Combine like terms: 4x + -2x = 2x
12 + 2x + x2 + -3x2 = -8 + 2x + 3x2 + 8 + -2x + -3x2

Combine like terms: x2 + -3x2 = -2x2
12 + 2x + -2x2 = -8 + 2x + 3x2 + 8 + -2x + -3x2

Reorder the terms:
12 + 2x + -2x2 = -8 + 8 + 2x + -2x + 3x2 + -3x2

Combine like terms: -8 + 8 = 0
12 + 2x + -2x2 = 0 + 2x + -2x + 3x2 + -3x2
12 + 2x + -2x2 = 2x + -2x + 3x2 + -3x2

Combine like terms: 2x + -2x = 0
12 + 2x + -2x2 = 0 + 3x2 + -3x2
12 + 2x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
12 + 2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + x + -1x2) = 0

Factor a trinomial.
2((3 + -1x)(2 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {3, -2}

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