(2x-5)(3x-4)=3x

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Solution for (2x-5)(3x-4)=3x equation: 


Simplifying
(2x + -5)(3x + -4) = 3x

Reorder the terms:
(-5 + 2x)(3x + -4) = 3x

Reorder the terms:
(-5 + 2x)(-4 + 3x) = 3x

Multiply (-5 + 2x) * (-4 + 3x)
(-5(-4 + 3x) + 2x * (-4 + 3x)) = 3x
((-4 * -5 + 3x * -5) + 2x * (-4 + 3x)) = 3x
((20 + -15x) + 2x * (-4 + 3x)) = 3x
(20 + -15x + (-4 * 2x + 3x * 2x)) = 3x
(20 + -15x + (-8x + 6x2)) = 3x

Combine like terms: -15x + -8x = -23x
(20 + -23x + 6x2) = 3x

Solving
20 + -23x + 6x2 = 3x

Solving for variable 'x'.

Reorder the terms:
20 + -23x + -3x + 6x2 = 3x + -3x

Combine like terms: -23x + -3x = -26x
20 + -26x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
20 + -26x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -13x + 3x2) = 0

Factor a trinomial.
2((1 + -1x)(10 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333
Solution
x = {1, 3.333333333}

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