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

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


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

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

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

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

Combine like terms: 3x + -10x = -7x
(-5 + -7x + 6x2) = 6x + -5

Reorder the terms:
-5 + -7x + 6x2 = -5 + 6x

Add '5' to each side of the equation.
-5 + -7x + 5 + 6x2 = -5 + 5 + 6x

Reorder the terms:
-5 + 5 + -7x + 6x2 = -5 + 5 + 6x

Combine like terms: -5 + 5 = 0
0 + -7x + 6x2 = -5 + 5 + 6x
-7x + 6x2 = -5 + 5 + 6x

Combine like terms: -5 + 5 = 0
-7x + 6x2 = 0 + 6x
-7x + 6x2 = 6x

Solving
-7x + 6x2 = 6x

Solving for variable 'x'.

Reorder the terms:
-7x + -6x + 6x2 = 6x + -6x

Combine like terms: -7x + -6x = -13x
-13x + 6x2 = 6x + -6x

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-13 + 6x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-13 + 6x)' equal to zero and attempt to solve:

Simplifying
-13 + 6x = 0

Solving
-13 + 6x = 0

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

Add '13' to each side of the equation.
-13 + 13 + 6x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 6x = 0 + 13
6x = 0 + 13

Combine like terms: 0 + 13 = 13
6x = 13

Divide each side by '6'.
x = 2.166666667

Simplifying
x = 2.166666667
Solution
x = {0, 2.166666667}

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