6x-3-(5-x)(2x-1)=0

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Solution for 6x-3-(5-x)(2x-1)=0 equation:


Simplifying
6x + -3 + -1(5 + -1x)(2x + -1) = 0

Reorder the terms:
6x + -3 + -1(5 + -1x)(-1 + 2x) = 0

Multiply (5 + -1x) * (-1 + 2x)
6x + -3 + -1(5(-1 + 2x) + -1x * (-1 + 2x)) = 0
6x + -3 + -1((-1 * 5 + 2x * 5) + -1x * (-1 + 2x)) = 0
6x + -3 + -1((-5 + 10x) + -1x * (-1 + 2x)) = 0
6x + -3 + -1(-5 + 10x + (-1 * -1x + 2x * -1x)) = 0
6x + -3 + -1(-5 + 10x + (1x + -2x2)) = 0

Combine like terms: 10x + 1x = 11x
6x + -3 + -1(-5 + 11x + -2x2) = 0
6x + -3 + (-5 * -1 + 11x * -1 + -2x2 * -1) = 0
6x + -3 + (5 + -11x + 2x2) = 0

Reorder the terms:
-3 + 5 + 6x + -11x + 2x2 = 0

Combine like terms: -3 + 5 = 2
2 + 6x + -11x + 2x2 = 0

Combine like terms: 6x + -11x = -5x
2 + -5x + 2x2 = 0

Solving
2 + -5x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -2x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.5, 2}

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