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

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

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

Reorder the terms:
x(-3 + 2x) + -2(3 + 2x) = -4(x + 1)
(-3 * x + 2x * x) + -2(3 + 2x) = -4(x + 1)
(-3x + 2x2) + -2(3 + 2x) = -4(x + 1)
-3x + 2x2 + (3 * -2 + 2x * -2) = -4(x + 1)
-3x + 2x2 + (-6 + -4x) = -4(x + 1)

Reorder the terms:
-6 + -3x + -4x + 2x2 = -4(x + 1)

Combine like terms: -3x + -4x = -7x
-6 + -7x + 2x2 = -4(x + 1)

Reorder the terms:
-6 + -7x + 2x2 = -4(1 + x)
-6 + -7x + 2x2 = (1 * -4 + x * -4)
-6 + -7x + 2x2 = (-4 + -4x)

Solving
-6 + -7x + 2x2 = -4 + -4x

Solving for variable 'x'.

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

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

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

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

Combine like terms: -4 + 4 = 0
-2 + -3x + 2x2 = 0 + -4x + 4x
-2 + -3x + 2x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-2 + -3x + 2x2 = 0

Factor a trinomial.
(-1 + -2x)(2 + -1x) = 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 '(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
Solution
x = {-0.5, 2}