(5x-3)(6x-4)=x

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Solution for (5x-3)(6x-4)=x equation: 


Simplifying
(5x + -3)(6x + -4) = x

Reorder the terms:
(-3 + 5x)(6x + -4) = x

Reorder the terms:
(-3 + 5x)(-4 + 6x) = x

Multiply (-3 + 5x) * (-4 + 6x)
(-3(-4 + 6x) + 5x * (-4 + 6x)) = x
((-4 * -3 + 6x * -3) + 5x * (-4 + 6x)) = x
((12 + -18x) + 5x * (-4 + 6x)) = x
(12 + -18x + (-4 * 5x + 6x * 5x)) = x
(12 + -18x + (-20x + 30x2)) = x

Combine like terms: -18x + -20x = -38x
(12 + -38x + 30x2) = x

Solving
12 + -38x + 30x2 = x

Solving for variable 'x'.

Reorder the terms:
12 + -38x + -1x + 30x2 = x + -1x

Combine like terms: -38x + -1x = -39x
12 + -39x + 30x2 = x + -1x

Combine like terms: x + -1x = 0
12 + -39x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -13x + 10x2) = 0

Factor a trinomial.
3((1 + -2x)(4 + -5x)) = 0

Ignore the factor 3.

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 '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {0.5, 0.8}

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