2x(x-3)-x(x-18)+35=0

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Solution for 2x(x-3)-x(x-18)+35=0 equation: 


Simplifying
2x(x + -3) + -1x(x + -18) + 35 = 0

Reorder the terms:
2x(-3 + x) + -1x(x + -18) + 35 = 0
(-3 * 2x + x * 2x) + -1x(x + -18) + 35 = 0
(-6x + 2x2) + -1x(x + -18) + 35 = 0

Reorder the terms:
-6x + 2x2 + -1x(-18 + x) + 35 = 0
-6x + 2x2 + (-18 * -1x + x * -1x) + 35 = 0
-6x + 2x2 + (18x + -1x2) + 35 = 0

Reorder the terms:
35 + -6x + 18x + 2x2 + -1x2 = 0

Combine like terms: -6x + 18x = 12x
35 + 12x + 2x2 + -1x2 = 0

Combine like terms: 2x2 + -1x2 = 1x2
35 + 12x + 1x2 = 0

Solving
35 + 12x + 1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + x)(5 + x) = 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {-7, -5}

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