x(10-3x)+6=x(4x-9)

Solution for x(10-3x)+6=x(4x-9) equation:

Simplifying
x(10 + -3x) + 6 = x(4x + -9)
(10 * x + -3x * x) + 6 = x(4x + -9)
(10x + -3x2) + 6 = x(4x + -9)

Reorder the terms:
6 + 10x + -3x2 = x(4x + -9)

Reorder the terms:
6 + 10x + -3x2 = x(-9 + 4x)
6 + 10x + -3x2 = (-9 * x + 4x * x)
6 + 10x + -3x2 = (-9x + 4x2)

Solving
6 + 10x + -3x2 = -9x + 4x2

Solving for variable 'x'.

Reorder the terms:
6 + 10x + 9x + -3x2 + -4x2 = -9x + 4x2 + 9x + -4x2

Combine like terms: 10x + 9x = 19x
6 + 19x + -3x2 + -4x2 = -9x + 4x2 + 9x + -4x2

Combine like terms: -3x2 + -4x2 = -7x2
6 + 19x + -7x2 = -9x + 4x2 + 9x + -4x2

Reorder the terms:
6 + 19x + -7x2 = -9x + 9x + 4x2 + -4x2

Combine like terms: -9x + 9x = 0
6 + 19x + -7x2 = 0 + 4x2 + -4x2
6 + 19x + -7x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + 19x + -7x2 = 0

Factor a trinomial.
(3 + -1x)(2 + 7x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(2 + 7x)' equal to zero and attempt to solve:

Simplifying
2 + 7x = 0

Solving
2 + 7x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7x = 0 + -2
7x = 0 + -2

Combine like terms: 0 + -2 = -2
7x = -2

Divide each side by '7'.
x = -0.2857142857

Simplifying
x = -0.2857142857
Solution
x = {3, -0.2857142857}