3-7x(3+4x)=-18

Solution for 3-7x(3+4x)=-18 equation:

Simplifying
3 + -7x(3 + 4x) = -18
3 + (3 * -7x + 4x * -7x) = -18
3 + (-21x + -28x2) = -18

Solving
3 + -21x + -28x2 = -18

Solving for variable 'x'.

Reorder the terms:
3 + 18 + -21x + -28x2 = -18 + 18

Combine like terms: 3 + 18 = 21
21 + -21x + -28x2 = -18 + 18

Combine like terms: -18 + 18 = 0
21 + -21x + -28x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(3 + -3x + -4x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(3 + -3x + -4x2)' equal to zero and attempt to solve:

Simplifying
3 + -3x + -4x2 = 0

Solving
3 + -3x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.75 + 0.75x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 0.75x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 0.75x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 0.75x + x2 = 0 + 0.75
0.75x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
0.75x + x2 = 0.75

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 0.75 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 0.75 + 0.140625

Combine like terms: 0.75 + 0.140625 = 0.890625
0.140625 + 0.75x + x2 = 0.890625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + 0.375) equal to 0.943729304 and -0.943729304.

Subproblem 1
x + 0.375 = 0.943729304

Simplifying
x + 0.375 = 0.943729304

Reorder the terms:
0.375 + x = 0.943729304

Solving
0.375 + x = 0.943729304

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 0.943729304 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 0.943729304 + -0.375
x = 0.943729304 + -0.375

Combine like terms: 0.943729304 + -0.375 = 0.568729304
x = 0.568729304

Simplifying
x = 0.568729304

Subproblem 2
x + 0.375 = -0.943729304

Simplifying
x + 0.375 = -0.943729304

Reorder the terms:
0.375 + x = -0.943729304

Solving
0.375 + x = -0.943729304

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -0.943729304 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -0.943729304 + -0.375
x = -0.943729304 + -0.375

Combine like terms: -0.943729304 + -0.375 = -1.318729304
x = -1.318729304

Simplifying
x = -1.318729304

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.568729304, -1.318729304}
Solution
x = {0.568729304, -1.318729304}