(x+14)(7x-18)=180

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Solution for (x+14)(7x-18)=180 equation: 


Simplifying
(x + 14)(7x + -18) = 180

Reorder the terms:
(14 + x)(7x + -18) = 180

Reorder the terms:
(14 + x)(-18 + 7x) = 180

Multiply (14 + x) * (-18 + 7x)
(14(-18 + 7x) + x(-18 + 7x)) = 180
((-18 * 14 + 7x * 14) + x(-18 + 7x)) = 180
((-252 + 98x) + x(-18 + 7x)) = 180
(-252 + 98x + (-18 * x + 7x * x)) = 180
(-252 + 98x + (-18x + 7x2)) = 180

Combine like terms: 98x + -18x = 80x
(-252 + 80x + 7x2) = 180

Solving
-252 + 80x + 7x2 = 180

Solving for variable 'x'.

Reorder the terms:
-252 + -180 + 80x + 7x2 = 180 + -180

Combine like terms: -252 + -180 = -432
-432 + 80x + 7x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-432 + 80x + 7x2 = 0

Factor a trinomial.
(-108 + -7x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-108 + -7x)' equal to zero and attempt to solve:

Simplifying
-108 + -7x = 0

Solving
-108 + -7x = 0

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

Add '108' to each side of the equation.
-108 + 108 + -7x = 0 + 108

Combine like terms: -108 + 108 = 0
0 + -7x = 0 + 108
-7x = 0 + 108

Combine like terms: 0 + 108 = 108
-7x = 108

Divide each side by '-7'.
x = -15.42857143

Simplifying
x = -15.42857143

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-15.42857143, 4}

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