0=(2x-7)(x-9)

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Solution for 0=(2x-7)(x-9) equation: 


Simplifying
0 = (2x + -7)(x + -9)

Reorder the terms:
0 = (-7 + 2x)(x + -9)

Reorder the terms:
0 = (-7 + 2x)(-9 + x)

Multiply (-7 + 2x) * (-9 + x)
0 = (-7(-9 + x) + 2x * (-9 + x))
0 = ((-9 * -7 + x * -7) + 2x * (-9 + x))
0 = ((63 + -7x) + 2x * (-9 + x))
0 = (63 + -7x + (-9 * 2x + x * 2x))
0 = (63 + -7x + (-18x + 2x2))

Combine like terms: -7x + -18x = -25x
0 = (63 + -25x + 2x2)

Solving
0 = 63 + -25x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -63 = -63
-63 + 25x + -2x2 = 63 + -25x + 2x2 + -63 + 25x + -2x2

Reorder the terms:
-63 + 25x + -2x2 = 63 + -63 + -25x + 25x + 2x2 + -2x2

Combine like terms: 63 + -63 = 0
-63 + 25x + -2x2 = 0 + -25x + 25x + 2x2 + -2x2
-63 + 25x + -2x2 = -25x + 25x + 2x2 + -2x2

Combine like terms: -25x + 25x = 0
-63 + 25x + -2x2 = 0 + 2x2 + -2x2
-63 + 25x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-63 + 25x + -2x2 = 0

Factor a trinomial.
(-9 + x)(7 + -2x) = 0


Subproblem 1
Set the factor '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

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

Add '9' to each side of the equation.
-9 + 9 + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Simplifying
x = 9

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

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

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

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {9, 3.5}

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