77=(x-3)(2x-9)

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Solution for 77=(x-3)(2x-9) equation: 


Simplifying
77 = (x + -3)(2x + -9)

Reorder the terms:
77 = (-3 + x)(2x + -9)

Reorder the terms:
77 = (-3 + x)(-9 + 2x)

Multiply (-3 + x) * (-9 + 2x)
77 = (-3(-9 + 2x) + x(-9 + 2x))
77 = ((-9 * -3 + 2x * -3) + x(-9 + 2x))
77 = ((27 + -6x) + x(-9 + 2x))
77 = (27 + -6x + (-9 * x + 2x * x))
77 = (27 + -6x + (-9x + 2x2))

Combine like terms: -6x + -9x = -15x
77 = (27 + -15x + 2x2)

Solving
77 = 27 + -15x + 2x2

Solving for variable 'x'.

Combine like terms: 77 + -27 = 50
50 + 15x + -2x2 = 27 + -15x + 2x2 + -27 + 15x + -2x2

Reorder the terms:
50 + 15x + -2x2 = 27 + -27 + -15x + 15x + 2x2 + -2x2

Combine like terms: 27 + -27 = 0
50 + 15x + -2x2 = 0 + -15x + 15x + 2x2 + -2x2
50 + 15x + -2x2 = -15x + 15x + 2x2 + -2x2

Combine like terms: -15x + 15x = 0
50 + 15x + -2x2 = 0 + 2x2 + -2x2
50 + 15x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
50 + 15x + -2x2 = 0

Factor a trinomial.
(10 + -1x)(5 + 2x) = 0


Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10

Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {10, -2.5}

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