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

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

Simplifying
x(2x + 7) + -3(x + -4) = 0

Reorder the terms:
x(7 + 2x) + -3(x + -4) = 0
(7 * x + 2x * x) + -3(x + -4) = 0
(7x + 2x2) + -3(x + -4) = 0

Reorder the terms:
7x + 2x2 + -3(-4 + x) = 0
7x + 2x2 + (-4 * -3 + x * -3) = 0
7x + 2x2 + (12 + -3x) = 0

Reorder the terms:
12 + 7x + -3x + 2x2 = 0

Combine like terms: 7x + -3x = 4x
12 + 4x + 2x2 = 0

Solving
12 + 4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
6 + 2x + x2 = 0

Solving
6 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 2x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 2x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 2x + x2 = 0 + -6
2x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
2x + x2 = -6

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -6 + 1

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

Combine like terms: -6 + 1 = -5
1 + 2x + x2 = -5

Factor a perfect square on the left side:
(x + 1)(x + 1) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.