5x+14=(3x-14)(3x-14)

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Solution for 5x+14=(3x-14)(3x-14) equation: 


Simplifying
5x + 14 = (3x + -14)(3x + -14)

Reorder the terms:
14 + 5x = (3x + -14)(3x + -14)

Reorder the terms:
14 + 5x = (-14 + 3x)(3x + -14)

Reorder the terms:
14 + 5x = (-14 + 3x)(-14 + 3x)

Multiply (-14 + 3x) * (-14 + 3x)
14 + 5x = (-14(-14 + 3x) + 3x * (-14 + 3x))
14 + 5x = ((-14 * -14 + 3x * -14) + 3x * (-14 + 3x))
14 + 5x = ((196 + -42x) + 3x * (-14 + 3x))
14 + 5x = (196 + -42x + (-14 * 3x + 3x * 3x))
14 + 5x = (196 + -42x + (-42x + 9x2))

Combine like terms: -42x + -42x = -84x
14 + 5x = (196 + -84x + 9x2)

Solving
14 + 5x = 196 + -84x + 9x2

Solving for variable 'x'.

Reorder the terms:
14 + -196 + 5x + 84x + -9x2 = 196 + -84x + 9x2 + -196 + 84x + -9x2

Combine like terms: 14 + -196 = -182
-182 + 5x + 84x + -9x2 = 196 + -84x + 9x2 + -196 + 84x + -9x2

Combine like terms: 5x + 84x = 89x
-182 + 89x + -9x2 = 196 + -84x + 9x2 + -196 + 84x + -9x2

Reorder the terms:
-182 + 89x + -9x2 = 196 + -196 + -84x + 84x + 9x2 + -9x2

Combine like terms: 196 + -196 = 0
-182 + 89x + -9x2 = 0 + -84x + 84x + 9x2 + -9x2
-182 + 89x + -9x2 = -84x + 84x + 9x2 + -9x2

Combine like terms: -84x + 84x = 0
-182 + 89x + -9x2 = 0 + 9x2 + -9x2
-182 + 89x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-182 + 89x + -9x2 = 0

Factor a trinomial.
(-7 + x)(26 + -9x) = 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 '(26 + -9x)' equal to zero and attempt to solve:

Simplifying
26 + -9x = 0

Solving
26 + -9x = 0

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

Add '-26' to each side of the equation.
26 + -26 + -9x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -9x = 0 + -26
-9x = 0 + -26

Combine like terms: 0 + -26 = -26
-9x = -26

Divide each side by '-9'.
x = 2.888888889

Simplifying
x = 2.888888889
Solution
x = {7, 2.888888889}

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