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

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


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

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

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

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

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

Reorder the terms:
3 + -4x + -4x2 = (4 + x)(2x + -1)

Reorder the terms:
3 + -4x + -4x2 = (4 + x)(-1 + 2x)

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

Combine like terms: 8x + -1x = 7x
3 + -4x + -4x2 = (-4 + 7x + 2x2)

Solving
3 + -4x + -4x2 = -4 + 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
3 + 4 + -4x + -7x + -4x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Combine like terms: 3 + 4 = 7
7 + -4x + -7x + -4x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Combine like terms: -4x + -7x = -11x
7 + -11x + -4x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Combine like terms: -4x2 + -2x2 = -6x2
7 + -11x + -6x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Reorder the terms:
7 + -11x + -6x2 = -4 + 4 + 7x + -7x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
7 + -11x + -6x2 = 0 + 7x + -7x + 2x2 + -2x2
7 + -11x + -6x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
7 + -11x + -6x2 = 0 + 2x2 + -2x2
7 + -11x + -6x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
7 + -11x + -6x2 = 0

Factor a trinomial.
(1 + -2x)(7 + 3x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {0.5, -2.333333333}

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