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

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


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

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

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

Multiply (-3 + 2x) * (-4 + 5x)
(-3(-4 + 5x) + 2x * (-4 + 5x)) = 0
((-4 * -3 + 5x * -3) + 2x * (-4 + 5x)) = 0
((12 + -15x) + 2x * (-4 + 5x)) = 0
(12 + -15x + (-4 * 2x + 5x * 2x)) = 0
(12 + -15x + (-8x + 10x2)) = 0

Combine like terms: -15x + -8x = -23x
(12 + -23x + 10x2) = 0

Solving
12 + -23x + 10x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -5x)(3 + -2x) = 0

Subproblem 1

Set the factor '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 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 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8

Subproblem 2

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {0.8, 1.5}

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