10x-7=5x(4x+6)

Solution for 10x-7=5x(4x+6) equation:

Simplifying
10x + -7 = 5x(4x + 6)

Reorder the terms:
-7 + 10x = 5x(4x + 6)

Reorder the terms:
-7 + 10x = 5x(6 + 4x)
-7 + 10x = (6 * 5x + 4x * 5x)
-7 + 10x = (30x + 20x2)

Solving
-7 + 10x = 30x + 20x2

Solving for variable 'x'.

Combine like terms: 10x + -30x = -20x
-7 + -20x + -20x2 = 30x + 20x2 + -30x + -20x2

Reorder the terms:
-7 + -20x + -20x2 = 30x + -30x + 20x2 + -20x2

Combine like terms: 30x + -30x = 0
-7 + -20x + -20x2 = 0 + 20x2 + -20x2
-7 + -20x + -20x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-7 + -20x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 20x + 20x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 20x + 20x2)' equal to zero and attempt to solve:

Simplifying
7 + 20x + 20x2 = 0

Solving
7 + 20x + 20x2 = 0

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

Divide each side by '20'.
0.35 + x + x2 = 0.0

Move the constant term to the right:

Add '-0.35' to each side of the equation.
0.35 + x + -0.35 + x2 = 0.0 + -0.35

Reorder the terms:
0.35 + -0.35 + x + x2 = 0.0 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + x + x2 = 0.0 + -0.35
x + x2 = 0.0 + -0.35

Combine like terms: 0.0 + -0.35 = -0.35
x + x2 = -0.35

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = -0.35 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -0.35 + 0.25

Combine like terms: -0.35 + 0.25 = -0.1
1.25 + x2 = -0.1

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.1

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.