(3x-2)*2+7=3x(2x-3)-(x+3)(x+3)+(-6+4x*2)

Solution for (3x-2)*2+7=3x(2x-3)-(x+3)(x+3)+(-6+4x*2) equation:

Simplifying
(3x + -2) * 2 + 7 = 3x(2x + -3) + -1(x + 3)(x + 3) + (-6 + 4x * 2)

Reorder the terms:
(-2 + 3x) * 2 + 7 = 3x(2x + -3) + -1(x + 3)(x + 3) + (-6 + 4x * 2)

Reorder the terms for easier multiplication:
2(-2 + 3x) + 7 = 3x(2x + -3) + -1(x + 3)(x + 3) + (-6 + 4x * 2)
(-2 * 2 + 3x * 2) + 7 = 3x(2x + -3) + -1(x + 3)(x + 3) + (-6 + 4x * 2)
(-4 + 6x) + 7 = 3x(2x + -3) + -1(x + 3)(x + 3) + (-6 + 4x * 2)

Reorder the terms:
-4 + 7 + 6x = 3x(2x + -3) + -1(x + 3)(x + 3) + (-6 + 4x * 2)

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

Reorder the terms:
3 + 6x = 3x(-3 + 2x) + -1(x + 3)(x + 3) + (-6 + 4x * 2)
3 + 6x = (-3 * 3x + 2x * 3x) + -1(x + 3)(x + 3) + (-6 + 4x * 2)
3 + 6x = (-9x + 6x2) + -1(x + 3)(x + 3) + (-6 + 4x * 2)

Reorder the terms:
3 + 6x = -9x + 6x2 + -1(3 + x)(x + 3) + (-6 + 4x * 2)

Reorder the terms:
3 + 6x = -9x + 6x2 + -1(3 + x)(3 + x) + (-6 + 4x * 2)

Multiply (3 + x) * (3 + x)
3 + 6x = -9x + 6x2 + -1(3(3 + x) + x(3 + x)) + (-6 + 4x * 2)
3 + 6x = -9x + 6x2 + -1((3 * 3 + x * 3) + x(3 + x)) + (-6 + 4x * 2)
3 + 6x = -9x + 6x2 + -1((9 + 3x) + x(3 + x)) + (-6 + 4x * 2)
3 + 6x = -9x + 6x2 + -1(9 + 3x + (3 * x + x * x)) + (-6 + 4x * 2)
3 + 6x = -9x + 6x2 + -1(9 + 3x + (3x + x2)) + (-6 + 4x * 2)

Combine like terms: 3x + 3x = 6x
3 + 6x = -9x + 6x2 + -1(9 + 6x + x2) + (-6 + 4x * 2)
3 + 6x = -9x + 6x2 + (9 * -1 + 6x * -1 + x2 * -1) + (-6 + 4x * 2)
3 + 6x = -9x + 6x2 + (-9 + -6x + -1x2) + (-6 + 4x * 2)

Reorder the terms for easier multiplication:
3 + 6x = -9x + 6x2 + -9 + -6x + -1x2 + (-6 + 4 * 2x)

Multiply 4 * 2
3 + 6x = -9x + 6x2 + -9 + -6x + -1x2 + (-6 + 8x)

Remove parenthesis around (-6 + 8x)
3 + 6x = -9x + 6x2 + -9 + -6x + -1x2 + -6 + 8x

Reorder the terms:
3 + 6x = -9 + -6 + -9x + -6x + 8x + 6x2 + -1x2

Combine like terms: -9 + -6 = -15
3 + 6x = -15 + -9x + -6x + 8x + 6x2 + -1x2

Combine like terms: -9x + -6x = -15x
3 + 6x = -15 + -15x + 8x + 6x2 + -1x2

Combine like terms: -15x + 8x = -7x
3 + 6x = -15 + -7x + 6x2 + -1x2

Combine like terms: 6x2 + -1x2 = 5x2
3 + 6x = -15 + -7x + 5x2

Solving
3 + 6x = -15 + -7x + 5x2

Solving for variable 'x'.

Reorder the terms:
3 + 15 + 6x + 7x + -5x2 = -15 + -7x + 5x2 + 15 + 7x + -5x2

Combine like terms: 3 + 15 = 18
18 + 6x + 7x + -5x2 = -15 + -7x + 5x2 + 15 + 7x + -5x2

Combine like terms: 6x + 7x = 13x
18 + 13x + -5x2 = -15 + -7x + 5x2 + 15 + 7x + -5x2

Reorder the terms:
18 + 13x + -5x2 = -15 + 15 + -7x + 7x + 5x2 + -5x2

Combine like terms: -15 + 15 = 0
18 + 13x + -5x2 = 0 + -7x + 7x + 5x2 + -5x2
18 + 13x + -5x2 = -7x + 7x + 5x2 + -5x2

Combine like terms: -7x + 7x = 0
18 + 13x + -5x2 = 0 + 5x2 + -5x2
18 + 13x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
18 + 13x + -5x2 = 0

Factor a trinomial.
(18 + -5x)(1 + x) = 0

Subproblem 1
Set the factor '(18 + -5x)' equal to zero and attempt to solve:

Simplifying
18 + -5x = 0

Solving
18 + -5x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -5x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -5x = 0 + -18
-5x = 0 + -18

Combine like terms: 0 + -18 = -18
-5x = -18

Divide each side by '-5'.
x = 3.6

Simplifying
x = 3.6
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 = {3.6, -1}