(2x-3)(3x-2)=21

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Solution for (2x-3)(3x-2)=21 equation:


Simplifying
(2x + -3)(3x + -2) = 21

Reorder the terms:
(-3 + 2x)(3x + -2) = 21

Reorder the terms:
(-3 + 2x)(-2 + 3x) = 21

Multiply (-3 + 2x) * (-2 + 3x)
(-3(-2 + 3x) + 2x * (-2 + 3x)) = 21
((-2 * -3 + 3x * -3) + 2x * (-2 + 3x)) = 21
((6 + -9x) + 2x * (-2 + 3x)) = 21
(6 + -9x + (-2 * 2x + 3x * 2x)) = 21
(6 + -9x + (-4x + 6x2)) = 21

Combine like terms: -9x + -4x = -13x
(6 + -13x + 6x2) = 21

Solving
6 + -13x + 6x2 = 21

Solving for variable 'x'.

Reorder the terms:
6 + -21 + -13x + 6x2 = 21 + -21

Combine like terms: 6 + -21 = -15
-15 + -13x + 6x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-15 + -13x + 6x2 = 0

Factor a trinomial.
(-5 + -6x)(3 + -1x) = 0

Subproblem 1

Set the factor '(-5 + -6x)' equal to zero and attempt to solve: Simplifying -5 + -6x = 0 Solving -5 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -6x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6x = 0 + 5 -6x = 0 + 5 Combine like terms: 0 + 5 = 5 -6x = 5 Divide each side by '-6'. x = -0.8333333333 Simplifying x = -0.8333333333

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 = {-0.8333333333, 3}

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