69=-3x(-2x+5)

Solution for 69=-3x(-2x+5) equation:

Simplifying
69 = -3x(-2x + 5)

Reorder the terms:
69 = -3x(5 + -2x)
69 = (5 * -3x + -2x * -3x)
69 = (-15x + 6x2)

Solving
69 = -15x + 6x2

Solving for variable 'x'.

Reorder the terms:
69 + 15x + -6x2 = -15x + 15x + 6x2 + -6x2

Combine like terms: -15x + 15x = 0
69 + 15x + -6x2 = 0 + 6x2 + -6x2
69 + 15x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
69 + 15x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(23 + 5x + -2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(23 + 5x + -2x2)' equal to zero and attempt to solve:

Simplifying
23 + 5x + -2x2 = 0

Solving
23 + 5x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-11.5 + -2.5x + x2 = 0

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + -2.5x + 11.5 + x2 = 0 + 11.5

Reorder the terms:
-11.5 + 11.5 + -2.5x + x2 = 0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + -2.5x + x2 = 0 + 11.5
-2.5x + x2 = 0 + 11.5

Combine like terms: 0 + 11.5 = 11.5
-2.5x + x2 = 11.5

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 11.5 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 11.5 + 1.5625

Combine like terms: 11.5 + 1.5625 = 13.0625
1.5625 + -2.5x + x2 = 13.0625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 13.0625

Calculate the square root of the right side: 3.614208074

Break this problem into two subproblems by setting 
(x + -1.25) equal to 3.614208074 and -3.614208074.

Subproblem 1
x + -1.25 = 3.614208074

Simplifying
x + -1.25 = 3.614208074

Reorder the terms:
-1.25 + x = 3.614208074

Solving
-1.25 + x = 3.614208074

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 3.614208074 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 3.614208074 + 1.25
x = 3.614208074 + 1.25

Combine like terms: 3.614208074 + 1.25 = 4.864208074
x = 4.864208074

Simplifying
x = 4.864208074

Subproblem 2
x + -1.25 = -3.614208074

Simplifying
x + -1.25 = -3.614208074

Reorder the terms:
-1.25 + x = -3.614208074

Solving
-1.25 + x = -3.614208074

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -3.614208074 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -3.614208074 + 1.25
x = -3.614208074 + 1.25

Combine like terms: -3.614208074 + 1.25 = -2.364208074
x = -2.364208074

Simplifying
x = -2.364208074

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.864208074, -2.364208074}
Solution
x = {4.864208074, -2.364208074}