(3x-4)(2x-5)=0

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Solution for (3x-4)(2x-5)=0 equation:


Simplifying
(3x + -4)(2x + -5) = 0

Reorder the terms:
(-4 + 3x)(2x + -5) = 0

Reorder the terms:
(-4 + 3x)(-5 + 2x) = 0

Multiply (-4 + 3x) * (-5 + 2x)
(-4(-5 + 2x) + 3x * (-5 + 2x)) = 0
((-5 * -4 + 2x * -4) + 3x * (-5 + 2x)) = 0
((20 + -8x) + 3x * (-5 + 2x)) = 0
(20 + -8x + (-5 * 3x + 2x * 3x)) = 0
(20 + -8x + (-15x + 6x2)) = 0

Combine like terms: -8x + -15x = -23x
(20 + -23x + 6x2) = 0

Solving
20 + -23x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -3x)(5 + -2x) = 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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {1.333333333, 2.5}

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