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

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


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

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

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

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

Combine like terms: -3x + -4x = -7x
0 = (12 + -7x + x2)

Solving
0 = 12 + -7x + x2

Solving for variable 'x'.

Combine like terms: 0 + -12 = -12
-12 + 7x + -1x2 = 12 + -7x + x2 + -12 + 7x + -1x2

Reorder the terms:
-12 + 7x + -1x2 = 12 + -12 + -7x + 7x + x2 + -1x2

Combine like terms: 12 + -12 = 0
-12 + 7x + -1x2 = 0 + -7x + 7x + x2 + -1x2
-12 + 7x + -1x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
-12 + 7x + -1x2 = 0 + x2 + -1x2
-12 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 7x + -1x2 = 0

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


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

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

Simplifying
x = 4

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {4, 3}

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