(x-3)(3x+4)=(x+2)(x-6)

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Solution for (x-3)(3x+4)=(x+2)(x-6) equation: 


Simplifying
(x + -3)(3x + 4) = (x + 2)(x + -6)

Reorder the terms:
(-3 + x)(3x + 4) = (x + 2)(x + -6)

Reorder the terms:
(-3 + x)(4 + 3x) = (x + 2)(x + -6)

Multiply (-3 + x) * (4 + 3x)
(-3(4 + 3x) + x(4 + 3x)) = (x + 2)(x + -6)
((4 * -3 + 3x * -3) + x(4 + 3x)) = (x + 2)(x + -6)
((-12 + -9x) + x(4 + 3x)) = (x + 2)(x + -6)
(-12 + -9x + (4 * x + 3x * x)) = (x + 2)(x + -6)
(-12 + -9x + (4x + 3x2)) = (x + 2)(x + -6)

Combine like terms: -9x + 4x = -5x
(-12 + -5x + 3x2) = (x + 2)(x + -6)

Reorder the terms:
-12 + -5x + 3x2 = (2 + x)(x + -6)

Reorder the terms:
-12 + -5x + 3x2 = (2 + x)(-6 + x)

Multiply (2 + x) * (-6 + x)
-12 + -5x + 3x2 = (2(-6 + x) + x(-6 + x))
-12 + -5x + 3x2 = ((-6 * 2 + x * 2) + x(-6 + x))
-12 + -5x + 3x2 = ((-12 + 2x) + x(-6 + x))
-12 + -5x + 3x2 = (-12 + 2x + (-6 * x + x * x))
-12 + -5x + 3x2 = (-12 + 2x + (-6x + x2))

Combine like terms: 2x + -6x = -4x
-12 + -5x + 3x2 = (-12 + -4x + x2)

Add '12' to each side of the equation.
-12 + -5x + 12 + 3x2 = -12 + -4x + 12 + x2

Reorder the terms:
-12 + 12 + -5x + 3x2 = -12 + -4x + 12 + x2

Combine like terms: -12 + 12 = 0
0 + -5x + 3x2 = -12 + -4x + 12 + x2
-5x + 3x2 = -12 + -4x + 12 + x2

Reorder the terms:
-5x + 3x2 = -12 + 12 + -4x + x2

Combine like terms: -12 + 12 = 0
-5x + 3x2 = 0 + -4x + x2
-5x + 3x2 = -4x + x2

Solving
-5x + 3x2 = -4x + x2

Solving for variable 'x'.

Reorder the terms:
-5x + 4x + 3x2 + -1x2 = -4x + x2 + 4x + -1x2

Combine like terms: -5x + 4x = -1x
-1x + 3x2 + -1x2 = -4x + x2 + 4x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-1x + 2x2 = -4x + x2 + 4x + -1x2

Reorder the terms:
-1x + 2x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
-1x + 2x2 = 0 + x2 + -1x2
-1x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 2x) = 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 '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x = 0 + 1
2x = 0 + 1

Combine like terms: 0 + 1 = 1
2x = 1

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, 0.5}

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