3(1-4x)-(5x+2)(7+x)=

Solution for 3(1-4x)-(5x+2)(7+x)= equation:

Simplifying
3(1 + -4x) + -1(5x + 2)(7 + x) = 0
(1 * 3 + -4x * 3) + -1(5x + 2)(7 + x) = 0
(3 + -12x) + -1(5x + 2)(7 + x) = 0

Reorder the terms:
3 + -12x + -1(2 + 5x)(7 + x) = 0

Multiply (2 + 5x) * (7 + x)
3 + -12x + -1(2(7 + x) + 5x * (7 + x)) = 0
3 + -12x + -1((7 * 2 + x * 2) + 5x * (7 + x)) = 0
3 + -12x + -1((14 + 2x) + 5x * (7 + x)) = 0
3 + -12x + -1(14 + 2x + (7 * 5x + x * 5x)) = 0
3 + -12x + -1(14 + 2x + (35x + 5x2)) = 0

Combine like terms: 2x + 35x = 37x
3 + -12x + -1(14 + 37x + 5x2) = 0
3 + -12x + (14 * -1 + 37x * -1 + 5x2 * -1) = 0
3 + -12x + (-14 + -37x + -5x2) = 0

Reorder the terms:
3 + -14 + -12x + -37x + -5x2 = 0

Combine like terms: 3 + -14 = -11
-11 + -12x + -37x + -5x2 = 0

Combine like terms: -12x + -37x = -49x
-11 + -49x + -5x2 = 0

Solving
-11 + -49x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(11 + 49x + 5x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(11 + 49x + 5x2)' equal to zero and attempt to solve:

Simplifying
11 + 49x + 5x2 = 0

Solving
11 + 49x + 5x2 = 0

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

Divide each side by '5'.
2.2 + 9.8x + x2 = 0

Move the constant term to the right:

Add '-2.2' to each side of the equation.
2.2 + 9.8x + -2.2 + x2 = 0 + -2.2

Reorder the terms:
2.2 + -2.2 + 9.8x + x2 = 0 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + 9.8x + x2 = 0 + -2.2
9.8x + x2 = 0 + -2.2

Combine like terms: 0 + -2.2 = -2.2
9.8x + x2 = -2.2

The x term is 9.8x.  Take half its coefficient (4.9).
Square it (24.01) and add it to both sides.

Add '24.01' to each side of the equation.
9.8x + 24.01 + x2 = -2.2 + 24.01

Reorder the terms:
24.01 + 9.8x + x2 = -2.2 + 24.01

Combine like terms: -2.2 + 24.01 = 21.81
24.01 + 9.8x + x2 = 21.81

Factor a perfect square on the left side:
(x + 4.9)(x + 4.9) = 21.81

Calculate the square root of the right side: 4.670117772

Break this problem into two subproblems by setting 
(x + 4.9) equal to 4.670117772 and -4.670117772.

Subproblem 1
x + 4.9 = 4.670117772

Simplifying
x + 4.9 = 4.670117772

Reorder the terms:
4.9 + x = 4.670117772

Solving
4.9 + x = 4.670117772

Solving for variable 'x'.

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

Add '-4.9' to each side of the equation.
4.9 + -4.9 + x = 4.670117772 + -4.9

Combine like terms: 4.9 + -4.9 = 0.0
0.0 + x = 4.670117772 + -4.9
x = 4.670117772 + -4.9

Combine like terms: 4.670117772 + -4.9 = -0.229882228
x = -0.229882228

Simplifying
x = -0.229882228

Subproblem 2
x + 4.9 = -4.670117772

Simplifying
x + 4.9 = -4.670117772

Reorder the terms:
4.9 + x = -4.670117772

Solving
4.9 + x = -4.670117772

Solving for variable 'x'.

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

Add '-4.9' to each side of the equation.
4.9 + -4.9 + x = -4.670117772 + -4.9

Combine like terms: 4.9 + -4.9 = 0.0
0.0 + x = -4.670117772 + -4.9
x = -4.670117772 + -4.9

Combine like terms: -4.670117772 + -4.9 = -9.570117772
x = -9.570117772

Simplifying
x = -9.570117772

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.229882228, -9.570117772}
Solution
x = {-0.229882228, -9.570117772}