(2x-1)(3x+1)-(5x+4*2x-1)=0

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Solution for (2x-1)(3x+1)-(5x+4*2x-1)=0 equation: 


Simplifying
(2x + -1)(3x + 1) + -1(5x + 4 * 2x + -1) = 0

Reorder the terms:
(-1 + 2x)(3x + 1) + -1(5x + 4 * 2x + -1) = 0

Reorder the terms:
(-1 + 2x)(1 + 3x) + -1(5x + 4 * 2x + -1) = 0

Multiply (-1 + 2x) * (1 + 3x)
(-1(1 + 3x) + 2x * (1 + 3x)) + -1(5x + 4 * 2x + -1) = 0
((1 * -1 + 3x * -1) + 2x * (1 + 3x)) + -1(5x + 4 * 2x + -1) = 0
((-1 + -3x) + 2x * (1 + 3x)) + -1(5x + 4 * 2x + -1) = 0
(-1 + -3x + (1 * 2x + 3x * 2x)) + -1(5x + 4 * 2x + -1) = 0
(-1 + -3x + (2x + 6x2)) + -1(5x + 4 * 2x + -1) = 0

Combine like terms: -3x + 2x = -1x
(-1 + -1x + 6x2) + -1(5x + 4 * 2x + -1) = 0

Multiply 4 * 2
-1 + -1x + 6x2 + -1(5x + 8x + -1) = 0

Reorder the terms:
-1 + -1x + 6x2 + -1(-1 + 5x + 8x) = 0

Combine like terms: 5x + 8x = 13x
-1 + -1x + 6x2 + -1(-1 + 13x) = 0
-1 + -1x + 6x2 + (-1 * -1 + 13x * -1) = 0
-1 + -1x + 6x2 + (1 + -13x) = 0

Reorder the terms:
-1 + 1 + -1x + -13x + 6x2 = 0

Combine like terms: -1 + 1 = 0
0 + -1x + -13x + 6x2 = 0
-1x + -13x + 6x2 = 0

Combine like terms: -1x + -13x = -14x
-14x + 6x2 = 0

Solving
-14x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-7 + 3x) = 0

Ignore the factor 2.

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 '(-7 + 3x)' equal to zero and attempt to solve:

Simplifying
-7 + 3x = 0

Solving
-7 + 3x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3x = 0 + 7
3x = 0 + 7

Combine like terms: 0 + 7 = 7
3x = 7

Divide each side by '3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {0, 2.333333333}

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