x(x+1)=10x-14

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Solution for x(x+1)=10x-14 equation: 


Simplifying
x(x + 1) = 10x + -14

Reorder the terms:
x(1 + x) = 10x + -14
(1 * x + x * x) = 10x + -14
(1x + x2) = 10x + -14

Reorder the terms:
1x + x2 = -14 + 10x

Solving
1x + x2 = -14 + 10x

Solving for variable 'x'.

Reorder the terms:
14 + 1x + -10x + x2 = -14 + 10x + 14 + -10x

Combine like terms: 1x + -10x = -9x
14 + -9x + x2 = -14 + 10x + 14 + -10x

Reorder the terms:
14 + -9x + x2 = -14 + 14 + 10x + -10x

Combine like terms: -14 + 14 = 0
14 + -9x + x2 = 0 + 10x + -10x
14 + -9x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
14 + -9x + x2 = 0

Factor a trinomial.
(2 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
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
Solution
x = {2, 7}

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