x(x+14)=7(4x-7)

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Solution for x(x+14)=7(4x-7) equation: 


Simplifying
x(x + 14) = 7(4x + -7)

Reorder the terms:
x(14 + x) = 7(4x + -7)
(14 * x + x * x) = 7(4x + -7)
(14x + x2) = 7(4x + -7)

Reorder the terms:
14x + x2 = 7(-7 + 4x)
14x + x2 = (-7 * 7 + 4x * 7)
14x + x2 = (-49 + 28x)

Solving
14x + x2 = -49 + 28x

Solving for variable 'x'.

Reorder the terms:
49 + 14x + -28x + x2 = -49 + 28x + 49 + -28x

Combine like terms: 14x + -28x = -14x
49 + -14x + x2 = -49 + 28x + 49 + -28x

Reorder the terms:
49 + -14x + x2 = -49 + 49 + 28x + -28x

Combine like terms: -49 + 49 = 0
49 + -14x + x2 = 0 + 28x + -28x
49 + -14x + x2 = 28x + -28x

Combine like terms: 28x + -28x = 0
49 + -14x + x2 = 0

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

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