X(2x-2)+x(2x-2)=(4x+6)(x-4)

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Solution for X(2x-2)+x(2x-2)=(4x+6)(x-4) equation:


Simplifying
X(2x + -2) + x(2x + -2) = (4x + 6)(x + -4)

Reorder the terms:
X(-2 + 2x) + x(2x + -2) = (4x + 6)(x + -4)
(-2 * X + 2x * X) + x(2x + -2) = (4x + 6)(x + -4)
(-2X + 2xX) + x(2x + -2) = (4x + 6)(x + -4)

Reorder the terms:
-2X + 2xX + x(-2 + 2x) = (4x + 6)(x + -4)
-2X + 2xX + (-2 * x + 2x * x) = (4x + 6)(x + -4)
-2X + 2xX + (-2x + 2x2) = (4x + 6)(x + -4)

Reorder the terms:
-2X + -2x + 2xX + 2x2 = (4x + 6)(x + -4)

Reorder the terms:
-2X + -2x + 2xX + 2x2 = (6 + 4x)(x + -4)

Reorder the terms:
-2X + -2x + 2xX + 2x2 = (6 + 4x)(-4 + x)

Multiply (6 + 4x) * (-4 + x)
-2X + -2x + 2xX + 2x2 = (6(-4 + x) + 4x * (-4 + x))
-2X + -2x + 2xX + 2x2 = ((-4 * 6 + x * 6) + 4x * (-4 + x))
-2X + -2x + 2xX + 2x2 = ((-24 + 6x) + 4x * (-4 + x))
-2X + -2x + 2xX + 2x2 = (-24 + 6x + (-4 * 4x + x * 4x))
-2X + -2x + 2xX + 2x2 = (-24 + 6x + (-16x + 4x2))

Combine like terms: 6x + -16x = -10x
-2X + -2x + 2xX + 2x2 = (-24 + -10x + 4x2)

Solving
-2X + -2x + 2xX + 2x2 = -24 + -10x + 4x2

Solving for variable 'X'.

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

Add '2x' to each side of the equation.
-2X + -2x + 2xX + 2x + 2x2 = -24 + -10x + 2x + 4x2

Reorder the terms:
-2X + -2x + 2x + 2xX + 2x2 = -24 + -10x + 2x + 4x2

Combine like terms: -2x + 2x = 0
-2X + 0 + 2xX + 2x2 = -24 + -10x + 2x + 4x2
-2X + 2xX + 2x2 = -24 + -10x + 2x + 4x2

Combine like terms: -10x + 2x = -8x
-2X + 2xX + 2x2 = -24 + -8x + 4x2

Add '-2x2' to each side of the equation.
-2X + 2xX + 2x2 + -2x2 = -24 + -8x + 4x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-2X + 2xX + 0 = -24 + -8x + 4x2 + -2x2
-2X + 2xX = -24 + -8x + 4x2 + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
-2X + 2xX = -24 + -8x + 2x2

Reorder the terms:
24 + -2X + 8x + 2xX + -2x2 = -24 + -8x + 2x2 + 24 + 8x + -2x2

Reorder the terms:
24 + -2X + 8x + 2xX + -2x2 = -24 + 24 + -8x + 8x + 2x2 + -2x2

Combine like terms: -24 + 24 = 0
24 + -2X + 8x + 2xX + -2x2 = 0 + -8x + 8x + 2x2 + -2x2
24 + -2X + 8x + 2xX + -2x2 = -8x + 8x + 2x2 + -2x2

Combine like terms: -8x + 8x = 0
24 + -2X + 8x + 2xX + -2x2 = 0 + 2x2 + -2x2
24 + -2X + 8x + 2xX + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
24 + -2X + 8x + 2xX + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -1X + 4x + xX + -1x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(12 + -1X + 4x + xX + -1x2)' equal to zero and attempt to solve: Simplifying 12 + -1X + 4x + xX + -1x2 = 0 Solving 12 + -1X + 4x + xX + -1x2 = 0 Move all terms containing X to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -1X + 4x + xX + -12 + -1x2 = 0 + -12 Reorder the terms: 12 + -12 + -1X + 4x + xX + -1x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1X + 4x + xX + -1x2 = 0 + -12 -1X + 4x + xX + -1x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -1X + 4x + xX + -1x2 = -12 Add '-4x' to each side of the equation. -1X + 4x + xX + -4x + -1x2 = -12 + -4x Reorder the terms: -1X + 4x + -4x + xX + -1x2 = -12 + -4x Combine like terms: 4x + -4x = 0 -1X + 0 + xX + -1x2 = -12 + -4x -1X + xX + -1x2 = -12 + -4x Add 'x2' to each side of the equation. -1X + xX + -1x2 + x2 = -12 + -4x + x2 Combine like terms: -1x2 + x2 = 0 -1X + xX + 0 = -12 + -4x + x2 -1X + xX = -12 + -4x + x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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