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

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

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

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

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

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

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

Solving
4 + 1x + 2x2 = 6 + 4x

Solving for variable 'x'.

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

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

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

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

Combine like terms: 6 + -6 = 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}