(2x+4)(2x+4)=100

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Solution for (2x+4)(2x+4)=100 equation: 


Simplifying
(2x + 4)(2x + 4) = 100

Reorder the terms:
(4 + 2x)(2x + 4) = 100

Reorder the terms:
(4 + 2x)(4 + 2x) = 100

Multiply (4 + 2x) * (4 + 2x)
(4(4 + 2x) + 2x * (4 + 2x)) = 100
((4 * 4 + 2x * 4) + 2x * (4 + 2x)) = 100
((16 + 8x) + 2x * (4 + 2x)) = 100
(16 + 8x + (4 * 2x + 2x * 2x)) = 100
(16 + 8x + (8x + 4x2)) = 100

Combine like terms: 8x + 8x = 16x
(16 + 16x + 4x2) = 100

Solving
16 + 16x + 4x2 = 100

Solving for variable 'x'.

Reorder the terms:
16 + -100 + 16x + 4x2 = 100 + -100

Combine like terms: 16 + -100 = -84
-84 + 16x + 4x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-84 + 16x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + 4x + x2) = 0

Factor a trinomial.
4((-7 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-7, 3}

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