(2x+7)(7-2x)=49+7x

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Solution for (2x+7)(7-2x)=49+7x equation: 


Simplifying
(2x + 7)(7 + -2x) = 49 + 7x

Reorder the terms:
(7 + 2x)(7 + -2x) = 49 + 7x

Multiply (7 + 2x) * (7 + -2x)
(7(7 + -2x) + 2x * (7 + -2x)) = 49 + 7x
((7 * 7 + -2x * 7) + 2x * (7 + -2x)) = 49 + 7x
((49 + -14x) + 2x * (7 + -2x)) = 49 + 7x
(49 + -14x + (7 * 2x + -2x * 2x)) = 49 + 7x
(49 + -14x + (14x + -4x2)) = 49 + 7x

Combine like terms: -14x + 14x = 0
(49 + 0 + -4x2) = 49 + 7x
(49 + -4x2) = 49 + 7x

Add '-49' to each side of the equation.
49 + -49 + -4x2 = 49 + -49 + 7x

Combine like terms: 49 + -49 = 0
0 + -4x2 = 49 + -49 + 7x
-4x2 = 49 + -49 + 7x

Combine like terms: 49 + -49 = 0
-4x2 = 0 + 7x
-4x2 = 7x

Solving
-4x2 = 7x

Solving for variable 'x'.

Reorder the terms:
-7x + -4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-7x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(7 + 4x) = 0

Ignore the factor -1.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 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 + 4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x = 0 + -7
4x = 0 + -7

Combine like terms: 0 + -7 = -7
4x = -7

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75
Solution
x = {0, -1.75}

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