(2X+1)(3X-4)-X=-4

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Solution for (2X+1)(3X-4)-X=-4 equation: 


Simplifying
(2X + 1)(3X + -4) + -1X = -4

Reorder the terms:
(1 + 2X)(3X + -4) + -1X = -4

Reorder the terms:
(1 + 2X)(-4 + 3X) + -1X = -4

Multiply (1 + 2X) * (-4 + 3X)
(1(-4 + 3X) + 2X * (-4 + 3X)) + -1X = -4
((-4 * 1 + 3X * 1) + 2X * (-4 + 3X)) + -1X = -4
((-4 + 3X) + 2X * (-4 + 3X)) + -1X = -4
(-4 + 3X + (-4 * 2X + 3X * 2X)) + -1X = -4
(-4 + 3X + (-8X + 6X2)) + -1X = -4

Combine like terms: 3X + -8X = -5X
(-4 + -5X + 6X2) + -1X = -4

Reorder the terms:
-4 + -5X + -1X + 6X2 = -4

Combine like terms: -5X + -1X = -6X
-4 + -6X + 6X2 = -4

Add '4' to each side of the equation.
-4 + -6X + 4 + 6X2 = -4 + 4

Reorder the terms:
-4 + 4 + -6X + 6X2 = -4 + 4

Combine like terms: -4 + 4 = 0
0 + -6X + 6X2 = -4 + 4
-6X + 6X2 = -4 + 4

Combine like terms: -4 + 4 = 0
-6X + 6X2 = 0

Solving
-6X + 6X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '6X'.
6X(-1 + X) = 0

Ignore the factor 6.

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 '(-1 + X)' equal to zero and attempt to solve:

Simplifying
-1 + X = 0

Solving
-1 + X = 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 + X = 0 + 1

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

Combine like terms: 0 + 1 = 1
X = 1

Simplifying
X = 1
Solution
X = {0, 1}

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