x^2-10x+35=7x-35

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Solution for x^2-10x+35=7x-35 equation: 


Simplifying
x2 + -10x + 35 = 7x + -35

Reorder the terms:
35 + -10x + x2 = 7x + -35

Reorder the terms:
35 + -10x + x2 = -35 + 7x

Solving
35 + -10x + x2 = -35 + 7x

Solving for variable 'x'.

Reorder the terms:
35 + 35 + -10x + -7x + x2 = -35 + 7x + 35 + -7x

Combine like terms: 35 + 35 = 70
70 + -10x + -7x + x2 = -35 + 7x + 35 + -7x

Combine like terms: -10x + -7x = -17x
70 + -17x + x2 = -35 + 7x + 35 + -7x

Reorder the terms:
70 + -17x + x2 = -35 + 35 + 7x + -7x

Combine like terms: -35 + 35 = 0
70 + -17x + x2 = 0 + 7x + -7x
70 + -17x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
70 + -17x + x2 = 0

Factor a trinomial.
(7 + -1x)(10 + -1x) = 0


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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 2
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
Solution
x = {7, 10}

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