(2x-3)(x-12)=0

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Solution for (2x-3)(x-12)=0 equation:


Simplifying
(2x + -3)(x + -12) = 0

Reorder the terms:
(-3 + 2x)(x + -12) = 0

Reorder the terms:
(-3 + 2x)(-12 + x) = 0

Multiply (-3 + 2x) * (-12 + x)
(-3(-12 + x) + 2x * (-12 + x)) = 0
((-12 * -3 + x * -3) + 2x * (-12 + x)) = 0
((36 + -3x) + 2x * (-12 + x)) = 0
(36 + -3x + (-12 * 2x + x * 2x)) = 0
(36 + -3x + (-24x + 2x2)) = 0

Combine like terms: -3x + -24x = -27x
(36 + -27x + 2x2) = 0

Solving
36 + -27x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -2x)(12 + -1x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12

Solution

x = {1.5, 12}

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