x(7x-10)=4x^2+x-6

Solution for x(7x-10)=4x^2+x-6 equation:

Simplifying
x(7x + -10) = 4x2 + x + -6

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

Reorder the terms:
-10x + 7x2 = -6 + x + 4x2

Solving
-10x + 7x2 = -6 + x + 4x2

Solving for variable 'x'.

Reorder the terms:
6 + -10x + -1x + 7x2 + -4x2 = -6 + x + 4x2 + 6 + -1x + -4x2

Combine like terms: -10x + -1x = -11x
6 + -11x + 7x2 + -4x2 = -6 + x + 4x2 + 6 + -1x + -4x2

Combine like terms: 7x2 + -4x2 = 3x2
6 + -11x + 3x2 = -6 + x + 4x2 + 6 + -1x + -4x2

Reorder the terms:
6 + -11x + 3x2 = -6 + 6 + x + -1x + 4x2 + -4x2

Combine like terms: -6 + 6 = 0
6 + -11x + 3x2 = 0 + x + -1x + 4x2 + -4x2
6 + -11x + 3x2 = x + -1x + 4x2 + -4x2

Combine like terms: x + -1x = 0
6 + -11x + 3x2 = 0 + 4x2 + -4x2
6 + -11x + 3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + -11x + 3x2 = 0

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

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Subproblem 2
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
Solution
x = {0.6666666667, 3}