(2x+1)(x+4)+(x+4)(3-5x)=0

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Solution for (2x+1)(x+4)+(x+4)(3-5x)=0 equation: 


Simplifying
(2x + 1)(x + 4) + (x + 4)(3 + -5x) = 0

Reorder the terms:
(1 + 2x)(x + 4) + (x + 4)(3 + -5x) = 0

Reorder the terms:
(1 + 2x)(4 + x) + (x + 4)(3 + -5x) = 0

Multiply (1 + 2x) * (4 + x)
(1(4 + x) + 2x * (4 + x)) + (x + 4)(3 + -5x) = 0
((4 * 1 + x * 1) + 2x * (4 + x)) + (x + 4)(3 + -5x) = 0
((4 + 1x) + 2x * (4 + x)) + (x + 4)(3 + -5x) = 0
(4 + 1x + (4 * 2x + x * 2x)) + (x + 4)(3 + -5x) = 0
(4 + 1x + (8x + 2x2)) + (x + 4)(3 + -5x) = 0

Combine like terms: 1x + 8x = 9x
(4 + 9x + 2x2) + (x + 4)(3 + -5x) = 0

Reorder the terms:
4 + 9x + 2x2 + (4 + x)(3 + -5x) = 0

Multiply (4 + x) * (3 + -5x)
4 + 9x + 2x2 + (4(3 + -5x) + x(3 + -5x)) = 0
4 + 9x + 2x2 + ((3 * 4 + -5x * 4) + x(3 + -5x)) = 0
4 + 9x + 2x2 + ((12 + -20x) + x(3 + -5x)) = 0
4 + 9x + 2x2 + (12 + -20x + (3 * x + -5x * x)) = 0
4 + 9x + 2x2 + (12 + -20x + (3x + -5x2)) = 0

Combine like terms: -20x + 3x = -17x
4 + 9x + 2x2 + (12 + -17x + -5x2) = 0

Reorder the terms:
4 + 12 + 9x + -17x + 2x2 + -5x2 = 0

Combine like terms: 4 + 12 = 16
16 + 9x + -17x + 2x2 + -5x2 = 0

Combine like terms: 9x + -17x = -8x
16 + -8x + 2x2 + -5x2 = 0

Combine like terms: 2x2 + -5x2 = -3x2
16 + -8x + -3x2 = 0

Solving
16 + -8x + -3x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
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
Solution
x = {1.333333333, -4}

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