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

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


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

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

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

Multiply (-1 + 2x) * (3 + x)
(-1(3 + x) + 2x * (3 + x)) = -2(x + 4)
((3 * -1 + x * -1) + 2x * (3 + x)) = -2(x + 4)
((-3 + -1x) + 2x * (3 + x)) = -2(x + 4)
(-3 + -1x + (3 * 2x + x * 2x)) = -2(x + 4)
(-3 + -1x + (6x + 2x2)) = -2(x + 4)

Combine like terms: -1x + 6x = 5x
(-3 + 5x + 2x2) = -2(x + 4)

Reorder the terms:
-3 + 5x + 2x2 = -2(4 + x)
-3 + 5x + 2x2 = (4 * -2 + x * -2)
-3 + 5x + 2x2 = (-8 + -2x)

Solving
-3 + 5x + 2x2 = -8 + -2x

Solving for variable 'x'.

Reorder the terms:
-3 + 8 + 5x + 2x + 2x2 = -8 + -2x + 8 + 2x

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

Combine like terms: 5x + 2x = 7x
5 + 7x + 2x2 = -8 + -2x + 8 + 2x

Reorder the terms:
5 + 7x + 2x2 = -8 + 8 + -2x + 2x

Combine like terms: -8 + 8 = 0
5 + 7x + 2x2 = 0 + -2x + 2x
5 + 7x + 2x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
5 + 7x + 2x2 = 0

Factor a trinomial.
(5 + 2x)(1 + 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 '(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 = {-2.5, -1}

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