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

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

Simplifying
(4 + x)(-3 + -6x) = -7 + 3x

Multiply (4 + x) * (-3 + -6x)
(4(-3 + -6x) + x(-3 + -6x)) = -7 + 3x
((-3 * 4 + -6x * 4) + x(-3 + -6x)) = -7 + 3x
((-12 + -24x) + x(-3 + -6x)) = -7 + 3x
(-12 + -24x + (-3 * x + -6x * x)) = -7 + 3x
(-12 + -24x + (-3x + -6x2)) = -7 + 3x

Combine like terms: -24x + -3x = -27x
(-12 + -27x + -6x2) = -7 + 3x

Solving
-12 + -27x + -6x2 = -7 + 3x

Solving for variable 'x'.

Reorder the terms:
-12 + 7 + -27x + -3x + -6x2 = -7 + 3x + 7 + -3x

Combine like terms: -12 + 7 = -5
-5 + -27x + -3x + -6x2 = -7 + 3x + 7 + -3x

Combine like terms: -27x + -3x = -30x
-5 + -30x + -6x2 = -7 + 3x + 7 + -3x

Reorder the terms:
-5 + -30x + -6x2 = -7 + 7 + 3x + -3x

Combine like terms: -7 + 7 = 0
-5 + -30x + -6x2 = 0 + 3x + -3x
-5 + -30x + -6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-5 + -30x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 30x + 6x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 30x + 6x2)' equal to zero and attempt to solve:

Simplifying
5 + 30x + 6x2 = 0

Solving
5 + 30x + 6x2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
0.8333333333 + 5x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + 5x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + 5x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + 5x + x2 = 0 + -0.8333333333
5x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
5x + x2 = -0.8333333333

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -0.8333333333 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -0.8333333333 + 6.25

Combine like terms: -0.8333333333 + 6.25 = 5.4166666667
6.25 + 5x + x2 = 5.4166666667

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 5.4166666667

Calculate the square root of the right side: 2.327373341

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.327373341 and -2.327373341.

Subproblem 1
x + 2.5 = 2.327373341

Simplifying
x + 2.5 = 2.327373341

Reorder the terms:
2.5 + x = 2.327373341

Solving
2.5 + x = 2.327373341

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.327373341 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.327373341 + -2.5
x = 2.327373341 + -2.5

Combine like terms: 2.327373341 + -2.5 = -0.172626659
x = -0.172626659

Simplifying
x = -0.172626659

Subproblem 2
x + 2.5 = -2.327373341

Simplifying
x + 2.5 = -2.327373341

Reorder the terms:
2.5 + x = -2.327373341

Solving
2.5 + x = -2.327373341

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.327373341 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.327373341 + -2.5
x = -2.327373341 + -2.5

Combine like terms: -2.327373341 + -2.5 = -4.827373341
x = -4.827373341

Simplifying
x = -4.827373341

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.172626659, -4.827373341}
Solution
x = {-0.172626659, -4.827373341}