4x(x-6)-x(x-2)=-24

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Solution for 4x(x-6)-x(x-2)=-24 equation: 


Simplifying
4x(x + -6) + -1x(x + -2) = -24

Reorder the terms:
4x(-6 + x) + -1x(x + -2) = -24
(-6 * 4x + x * 4x) + -1x(x + -2) = -24
(-24x + 4x2) + -1x(x + -2) = -24

Reorder the terms:
-24x + 4x2 + -1x(-2 + x) = -24
-24x + 4x2 + (-2 * -1x + x * -1x) = -24
-24x + 4x2 + (2x + -1x2) = -24

Reorder the terms:
-24x + 2x + 4x2 + -1x2 = -24

Combine like terms: -24x + 2x = -22x
-22x + 4x2 + -1x2 = -24

Combine like terms: 4x2 + -1x2 = 3x2
-22x + 3x2 = -24

Solving
-22x + 3x2 = -24

Solving for variable 'x'.

Reorder the terms:
24 + -22x + 3x2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + -22x + 3x2 = 0

Factor a trinomial.
(4 + -3x)(6 + -1x) = 0


Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {1.333333333, 6}

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