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

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


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

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

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

Multiply (3 + 2x) * (4 + x)
(3(4 + x) + 2x * (4 + x)) = 2(x + -1) + 4
((4 * 3 + x * 3) + 2x * (4 + x)) = 2(x + -1) + 4
((12 + 3x) + 2x * (4 + x)) = 2(x + -1) + 4
(12 + 3x + (4 * 2x + x * 2x)) = 2(x + -1) + 4
(12 + 3x + (8x + 2x2)) = 2(x + -1) + 4

Combine like terms: 3x + 8x = 11x
(12 + 11x + 2x2) = 2(x + -1) + 4

Reorder the terms:
12 + 11x + 2x2 = 2(-1 + x) + 4
12 + 11x + 2x2 = (-1 * 2 + x * 2) + 4
12 + 11x + 2x2 = (-2 + 2x) + 4

Reorder the terms:
12 + 11x + 2x2 = -2 + 4 + 2x

Combine like terms: -2 + 4 = 2
12 + 11x + 2x2 = 2 + 2x

Solving
12 + 11x + 2x2 = 2 + 2x

Solving for variable 'x'.

Reorder the terms:
12 + -2 + 11x + -2x + 2x2 = 2 + 2x + -2 + -2x

Combine like terms: 12 + -2 = 10
10 + 11x + -2x + 2x2 = 2 + 2x + -2 + -2x

Combine like terms: 11x + -2x = 9x
10 + 9x + 2x2 = 2 + 2x + -2 + -2x

Reorder the terms:
10 + 9x + 2x2 = 2 + -2 + 2x + -2x

Combine like terms: 2 + -2 = 0
10 + 9x + 2x2 = 0 + 2x + -2x
10 + 9x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
10 + 9x + 2x2 = 0

Factor a trinomial.
(5 + 2x)(2 + x) = 0


Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, -2}

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