5x(7x-9)-10=

Solution for 5x(7x-9)-10= equation:

Simplifying
5x(7x + -9) + -10 = 0

Reorder the terms:
5x(-9 + 7x) + -10 = 0
(-9 * 5x + 7x * 5x) + -10 = 0
(-45x + 35x2) + -10 = 0

Reorder the terms:
-10 + -45x + 35x2 = 0

Solving
-10 + -45x + 35x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + -9x + 7x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-2 + -9x + 7x2)' equal to zero and attempt to solve:

Simplifying
-2 + -9x + 7x2 = 0

Solving
-2 + -9x + 7x2 = 0

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

Divide each side by '7'.
-0.2857142857 + -1.285714286x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -1.285714286x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -1.285714286x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -1.285714286x + x2 = 0 + 0.2857142857
-1.285714286x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-1.285714286x + x2 = 0.2857142857

The x term is -1.285714286x.  Take half its coefficient (-0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
-1.285714286x + 0.4132653063 + x2 = 0.2857142857 + 0.4132653063

Reorder the terms:
0.4132653063 + -1.285714286x + x2 = 0.2857142857 + 0.4132653063

Combine like terms: 0.2857142857 + 0.4132653063 = 0.698979592
0.4132653063 + -1.285714286x + x2 = 0.698979592

Factor a perfect square on the left side:
(x + -0.642857143)(x + -0.642857143) = 0.698979592

Calculate the square root of the right side: 0.836049994

Break this problem into two subproblems by setting 
(x + -0.642857143) equal to 0.836049994 and -0.836049994.

Subproblem 1
x + -0.642857143 = 0.836049994

Simplifying
x + -0.642857143 = 0.836049994

Reorder the terms:
-0.642857143 + x = 0.836049994

Solving
-0.642857143 + x = 0.836049994

Solving for variable 'x'.

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

Add '0.642857143' to each side of the equation.
-0.642857143 + 0.642857143 + x = 0.836049994 + 0.642857143

Combine like terms: -0.642857143 + 0.642857143 = 0.000000000
0.000000000 + x = 0.836049994 + 0.642857143
x = 0.836049994 + 0.642857143

Combine like terms: 0.836049994 + 0.642857143 = 1.478907137
x = 1.478907137

Simplifying
x = 1.478907137

Subproblem 2
x + -0.642857143 = -0.836049994

Simplifying
x + -0.642857143 = -0.836049994

Reorder the terms:
-0.642857143 + x = -0.836049994

Solving
-0.642857143 + x = -0.836049994

Solving for variable 'x'.

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

Add '0.642857143' to each side of the equation.
-0.642857143 + 0.642857143 + x = -0.836049994 + 0.642857143

Combine like terms: -0.642857143 + 0.642857143 = 0.000000000
0.000000000 + x = -0.836049994 + 0.642857143
x = -0.836049994 + 0.642857143

Combine like terms: -0.836049994 + 0.642857143 = -0.193192851
x = -0.193192851

Simplifying
x = -0.193192851

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.478907137, -0.193192851}
Solution
x = {1.478907137, -0.193192851}