x(2x-5)=35-14x

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Solution for x(2x-5)=35-14x equation: 


Simplifying
x(2x + -5) = 35 + -14x

Reorder the terms:
x(-5 + 2x) = 35 + -14x
(-5 * x + 2x * x) = 35 + -14x
(-5x + 2x2) = 35 + -14x

Solving
-5x + 2x2 = 35 + -14x

Solving for variable 'x'.

Reorder the terms:
-35 + -5x + 14x + 2x2 = 35 + -14x + -35 + 14x

Combine like terms: -5x + 14x = 9x
-35 + 9x + 2x2 = 35 + -14x + -35 + 14x

Reorder the terms:
-35 + 9x + 2x2 = 35 + -35 + -14x + 14x

Combine like terms: 35 + -35 = 0
-35 + 9x + 2x2 = 0 + -14x + 14x
-35 + 9x + 2x2 = -14x + 14x

Combine like terms: -14x + 14x = 0
-35 + 9x + 2x2 = 0

Factor a trinomial.
(-7 + -1x)(5 + -2x) = 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 '(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 = {-7, 2.5}

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