(2x-1)(x-3)=18

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Solution for (2x-1)(x-3)=18 equation:


Simplifying
(2x + -1)(x + -3) = 18

Reorder the terms:
(-1 + 2x)(x + -3) = 18

Reorder the terms:
(-1 + 2x)(-3 + x) = 18

Multiply (-1 + 2x) * (-3 + x)
(-1(-3 + x) + 2x * (-3 + x)) = 18
((-3 * -1 + x * -1) + 2x * (-3 + x)) = 18
((3 + -1x) + 2x * (-3 + x)) = 18
(3 + -1x + (-3 * 2x + x * 2x)) = 18
(3 + -1x + (-6x + 2x2)) = 18

Combine like terms: -1x + -6x = -7x
(3 + -7x + 2x2) = 18

Solving
3 + -7x + 2x2 = 18

Solving for variable 'x'.

Reorder the terms:
3 + -18 + -7x + 2x2 = 18 + -18

Combine like terms: 3 + -18 = -15
-15 + -7x + 2x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-15 + -7x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {-1.5, 5}

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