(2x-5)(x-6)=0

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Solution for (2x-5)(x-6)=0 equation:


Simplifying
(2x + -5)(x + -6) = 0

Reorder the terms:
(-5 + 2x)(x + -6) = 0

Reorder the terms:
(-5 + 2x)(-6 + x) = 0

Multiply (-5 + 2x) * (-6 + x)
(-5(-6 + x) + 2x * (-6 + x)) = 0
((-6 * -5 + x * -5) + 2x * (-6 + x)) = 0
((30 + -5x) + 2x * (-6 + x)) = 0
(30 + -5x + (-6 * 2x + x * 2x)) = 0
(30 + -5x + (-12x + 2x2)) = 0

Combine like terms: -5x + -12x = -17x
(30 + -17x + 2x2) = 0

Solving
30 + -17x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -2x)(6 + -1x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {2.5, 6}

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