(2x-3)*(x-5)=9

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Solution for (2x-3)*(x-5)=9 equation:


Simplifying
(2x + -3)(x + -5) = 9

Reorder the terms:
(-3 + 2x)(x + -5) = 9

Reorder the terms:
(-3 + 2x)(-5 + x) = 9

Multiply (-3 + 2x) * (-5 + x)
(-3(-5 + x) + 2x * (-5 + x)) = 9
((-5 * -3 + x * -3) + 2x * (-5 + x)) = 9
((15 + -3x) + 2x * (-5 + x)) = 9
(15 + -3x + (-5 * 2x + x * 2x)) = 9
(15 + -3x + (-10x + 2x2)) = 9

Combine like terms: -3x + -10x = -13x
(15 + -13x + 2x2) = 9

Solving
15 + -13x + 2x2 = 9

Solving for variable 'x'.

Reorder the terms:
15 + -9 + -13x + 2x2 = 9 + -9

Combine like terms: 15 + -9 = 6
6 + -13x + 2x2 = 9 + -9

Combine like terms: 9 + -9 = 0
6 + -13x + 2x2 = 0

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

Subproblem 1

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

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 = {0.5, 6}

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