(4x+7)(3x+4)=(x+2)(x+4)

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Solution for (4x+7)(3x+4)=(x+2)(x+4) equation: 


Simplifying
(4x + 7)(3x + 4) = (x + 2)(x + 4)

Reorder the terms:
(7 + 4x)(3x + 4) = (x + 2)(x + 4)

Reorder the terms:
(7 + 4x)(4 + 3x) = (x + 2)(x + 4)

Multiply (7 + 4x) * (4 + 3x)
(7(4 + 3x) + 4x * (4 + 3x)) = (x + 2)(x + 4)
((4 * 7 + 3x * 7) + 4x * (4 + 3x)) = (x + 2)(x + 4)
((28 + 21x) + 4x * (4 + 3x)) = (x + 2)(x + 4)
(28 + 21x + (4 * 4x + 3x * 4x)) = (x + 2)(x + 4)
(28 + 21x + (16x + 12x2)) = (x + 2)(x + 4)

Combine like terms: 21x + 16x = 37x
(28 + 37x + 12x2) = (x + 2)(x + 4)

Reorder the terms:
28 + 37x + 12x2 = (2 + x)(x + 4)

Reorder the terms:
28 + 37x + 12x2 = (2 + x)(4 + x)

Multiply (2 + x) * (4 + x)
28 + 37x + 12x2 = (2(4 + x) + x(4 + x))
28 + 37x + 12x2 = ((4 * 2 + x * 2) + x(4 + x))
28 + 37x + 12x2 = ((8 + 2x) + x(4 + x))
28 + 37x + 12x2 = (8 + 2x + (4 * x + x * x))
28 + 37x + 12x2 = (8 + 2x + (4x + x2))

Combine like terms: 2x + 4x = 6x
28 + 37x + 12x2 = (8 + 6x + x2)

Solving
28 + 37x + 12x2 = 8 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
28 + -8 + 37x + -6x + 12x2 + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Combine like terms: 28 + -8 = 20
20 + 37x + -6x + 12x2 + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Combine like terms: 37x + -6x = 31x
20 + 31x + 12x2 + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Combine like terms: 12x2 + -1x2 = 11x2
20 + 31x + 11x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Reorder the terms:
20 + 31x + 11x2 = 8 + -8 + 6x + -6x + x2 + -1x2

Combine like terms: 8 + -8 = 0
20 + 31x + 11x2 = 0 + 6x + -6x + x2 + -1x2
20 + 31x + 11x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
20 + 31x + 11x2 = 0 + x2 + -1x2
20 + 31x + 11x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + 31x + 11x2 = 0

Factor a trinomial.
(20 + 11x)(1 + x) = 0


Subproblem 1
Set the factor '(20 + 11x)' equal to zero and attempt to solve:

Simplifying
20 + 11x = 0

Solving
20 + 11x = 0

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

Add '-20' to each side of the equation.
20 + -20 + 11x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 11x = 0 + -20
11x = 0 + -20

Combine like terms: 0 + -20 = -20
11x = -20

Divide each side by '11'.
x = -1.818181818

Simplifying
x = -1.818181818

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-1.818181818, -1}

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