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

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


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

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

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

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

Combine like terms: 16x + 3x = 19x
(12 + 19x + 4x2) = (x + 7)(3x + 4)

Reorder the terms:
12 + 19x + 4x2 = (7 + x)(3x + 4)

Reorder the terms:
12 + 19x + 4x2 = (7 + x)(4 + 3x)

Multiply (7 + x) * (4 + 3x)
12 + 19x + 4x2 = (7(4 + 3x) + x(4 + 3x))
12 + 19x + 4x2 = ((4 * 7 + 3x * 7) + x(4 + 3x))
12 + 19x + 4x2 = ((28 + 21x) + x(4 + 3x))
12 + 19x + 4x2 = (28 + 21x + (4 * x + 3x * x))
12 + 19x + 4x2 = (28 + 21x + (4x + 3x2))

Combine like terms: 21x + 4x = 25x
12 + 19x + 4x2 = (28 + 25x + 3x2)

Solving
12 + 19x + 4x2 = 28 + 25x + 3x2

Solving for variable 'x'.

Reorder the terms:
12 + -28 + 19x + -25x + 4x2 + -3x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2

Combine like terms: 12 + -28 = -16
-16 + 19x + -25x + 4x2 + -3x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2

Combine like terms: 19x + -25x = -6x
-16 + -6x + 4x2 + -3x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-16 + -6x + 1x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2

Reorder the terms:
-16 + -6x + 1x2 = 28 + -28 + 25x + -25x + 3x2 + -3x2

Combine like terms: 28 + -28 = 0
-16 + -6x + 1x2 = 0 + 25x + -25x + 3x2 + -3x2
-16 + -6x + 1x2 = 25x + -25x + 3x2 + -3x2

Combine like terms: 25x + -25x = 0
-16 + -6x + 1x2 = 0 + 3x2 + -3x2
-16 + -6x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-16 + -6x + 1x2 = 0

Factor a trinomial.
(-2 + -1x)(8 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-2, 8}

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