5x(x-6)+3=-7

Solution for 5x(x-6)+3=-7 equation:

Simplifying
5x(x + -6) + 3 = -7

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

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

Solving
3 + -30x + 5x2 = -7

Solving for variable 'x'.

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

Combine like terms: 3 + 7 = 10
10 + -30x + 5x2 = -7 + 7

Combine like terms: -7 + 7 = 0
10 + -30x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -6x + x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(2 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
2 + -6x + x2 = 0

Solving
2 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -2 + 9

Reorder the terms:
9 + -6x + x2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + -6x + x2 = 7

Factor a perfect square on the left side:
(x + -3)(x + -3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -3) equal to 2.645751311 and -2.645751311.

Subproblem 1
x + -3 = 2.645751311

Simplifying
x + -3 = 2.645751311

Reorder the terms:
-3 + x = 2.645751311

Solving
-3 + x = 2.645751311

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.645751311 + 3
x = 2.645751311 + 3

Combine like terms: 2.645751311 + 3 = 5.645751311
x = 5.645751311

Simplifying
x = 5.645751311

Subproblem 2
x + -3 = -2.645751311

Simplifying
x + -3 = -2.645751311

Reorder the terms:
-3 + x = -2.645751311

Solving
-3 + x = -2.645751311

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.645751311 + 3
x = -2.645751311 + 3

Combine like terms: -2.645751311 + 3 = 0.354248689
x = 0.354248689

Simplifying
x = 0.354248689

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.645751311, 0.354248689}
Solution
x = {5.645751311, 0.354248689}