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

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


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

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

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

Multiply (-4 + x) * (2 + 3x)
0 = (-4(2 + 3x) + x(2 + 3x))
0 = ((2 * -4 + 3x * -4) + x(2 + 3x))
0 = ((-8 + -12x) + x(2 + 3x))
0 = (-8 + -12x + (2 * x + 3x * x))
0 = (-8 + -12x + (2x + 3x2))

Combine like terms: -12x + 2x = -10x
0 = (-8 + -10x + 3x2)

Solving
0 = -8 + -10x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 8 = 8
8 + 10x + -3x2 = -8 + -10x + 3x2 + 8 + 10x + -3x2

Reorder the terms:
8 + 10x + -3x2 = -8 + 8 + -10x + 10x + 3x2 + -3x2

Combine like terms: -8 + 8 = 0
8 + 10x + -3x2 = 0 + -10x + 10x + 3x2 + -3x2
8 + 10x + -3x2 = -10x + 10x + 3x2 + -3x2

Combine like terms: -10x + 10x = 0
8 + 10x + -3x2 = 0 + 3x2 + -3x2
8 + 10x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
8 + 10x + -3x2 = 0

Factor a trinomial.
(4 + -1x)(2 + 3x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {4, -0.6666666667}

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