0=(2x-1)(x-7)

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Solution for 0=(2x-1)(x-7) equation: 


Simplifying
0 = (2x + -1)(x + -7)

Reorder the terms:
0 = (-1 + 2x)(x + -7)

Reorder the terms:
0 = (-1 + 2x)(-7 + x)

Multiply (-1 + 2x) * (-7 + x)
0 = (-1(-7 + x) + 2x * (-7 + x))
0 = ((-7 * -1 + x * -1) + 2x * (-7 + x))
0 = ((7 + -1x) + 2x * (-7 + x))
0 = (7 + -1x + (-7 * 2x + x * 2x))
0 = (7 + -1x + (-14x + 2x2))

Combine like terms: -1x + -14x = -15x
0 = (7 + -15x + 2x2)

Solving
0 = 7 + -15x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -7 = -7
-7 + 15x + -2x2 = 7 + -15x + 2x2 + -7 + 15x + -2x2

Reorder the terms:
-7 + 15x + -2x2 = 7 + -7 + -15x + 15x + 2x2 + -2x2

Combine like terms: 7 + -7 = 0
-7 + 15x + -2x2 = 0 + -15x + 15x + 2x2 + -2x2
-7 + 15x + -2x2 = -15x + 15x + 2x2 + -2x2

Combine like terms: -15x + 15x = 0
-7 + 15x + -2x2 = 0 + 2x2 + -2x2
-7 + 15x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-7 + 15x + -2x2 = 0

Factor a trinomial.
(-7 + x)(1 + -2x) = 0


Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7

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 = {7, 0.5}

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