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

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


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

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

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

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

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

Solving
x = 12 + -7x + x2

Solving for variable 'x'.

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

Combine like terms: x + 7x = 8x
-12 + 8x + -1x2 = 12 + -7x + x2 + -12 + 7x + -1x2

Reorder the terms:
-12 + 8x + -1x2 = 12 + -12 + -7x + 7x + x2 + -1x2

Combine like terms: 12 + -12 = 0
-12 + 8x + -1x2 = 0 + -7x + 7x + x2 + -1x2
-12 + 8x + -1x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
-12 + 8x + -1x2 = 0 + x2 + -1x2
-12 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 8x + -1x2 = 0

Factor a trinomial.
(-6 + x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6

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

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {6, 2}

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