(2x-3)(3x-1)=24

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Solution for (2x-3)(3x-1)=24 equation:


Simplifying
(2x + -3)(3x + -1) = 24

Reorder the terms:
(-3 + 2x)(3x + -1) = 24

Reorder the terms:
(-3 + 2x)(-1 + 3x) = 24

Multiply (-3 + 2x) * (-1 + 3x)
(-3(-1 + 3x) + 2x * (-1 + 3x)) = 24
((-1 * -3 + 3x * -3) + 2x * (-1 + 3x)) = 24
((3 + -9x) + 2x * (-1 + 3x)) = 24
(3 + -9x + (-1 * 2x + 3x * 2x)) = 24
(3 + -9x + (-2x + 6x2)) = 24

Combine like terms: -9x + -2x = -11x
(3 + -11x + 6x2) = 24

Solving
3 + -11x + 6x2 = 24

Solving for variable 'x'.

Reorder the terms:
3 + -24 + -11x + 6x2 = 24 + -24

Combine like terms: 3 + -24 = -21
-21 + -11x + 6x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-21 + -11x + 6x2 = 0

Factor a trinomial.
(-7 + -6x)(3 + -1x) = 0

Subproblem 1

Set the factor '(-7 + -6x)' equal to zero and attempt to solve: Simplifying -7 + -6x = 0 Solving -7 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -6x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6x = 0 + 7 -6x = 0 + 7 Combine like terms: 0 + 7 = 7 -6x = 7 Divide each side by '-6'. x = -1.166666667 Simplifying x = -1.166666667

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 = {-1.166666667, 3}

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