(x-14)(x-14)=7x

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Solution for (x-14)(x-14)=7x equation: 


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

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

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

Multiply (-14 + x) * (-14 + x)
(-14(-14 + x) + x(-14 + x)) = 7x
((-14 * -14 + x * -14) + x(-14 + x)) = 7x
((196 + -14x) + x(-14 + x)) = 7x
(196 + -14x + (-14 * x + x * x)) = 7x
(196 + -14x + (-14x + x2)) = 7x

Combine like terms: -14x + -14x = -28x
(196 + -28x + x2) = 7x

Solving
196 + -28x + x2 = 7x

Solving for variable 'x'.

Reorder the terms:
196 + -28x + -7x + x2 = 7x + -7x

Combine like terms: -28x + -7x = -35x
196 + -35x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
196 + -35x + x2 = 0

Factor a trinomial.
(7 + -1x)(28 + -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 '(28 + -1x)' equal to zero and attempt to solve:

Simplifying
28 + -1x = 0

Solving
28 + -1x = 0

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

Add '-28' to each side of the equation.
28 + -28 + -1x = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -1x = 0 + -28
-1x = 0 + -28

Combine like terms: 0 + -28 = -28
-1x = -28

Divide each side by '-1'.
x = 28

Simplifying
x = 28
Solution
x = {7, 28}

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