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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