(42+2x)(8+2x)=672

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Solution for (42+2x)(8+2x)=672 equation: 


Simplifying
(42 + 2x)(8 + 2x) = 672

Multiply (42 + 2x) * (8 + 2x)
(42(8 + 2x) + 2x * (8 + 2x)) = 672
((8 * 42 + 2x * 42) + 2x * (8 + 2x)) = 672
((336 + 84x) + 2x * (8 + 2x)) = 672
(336 + 84x + (8 * 2x + 2x * 2x)) = 672
(336 + 84x + (16x + 4x2)) = 672

Combine like terms: 84x + 16x = 100x
(336 + 100x + 4x2) = 672

Solving
336 + 100x + 4x2 = 672

Solving for variable 'x'.

Reorder the terms:
336 + -672 + 100x + 4x2 = 672 + -672

Combine like terms: 336 + -672 = -336
-336 + 100x + 4x2 = 672 + -672

Combine like terms: 672 + -672 = 0
-336 + 100x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-84 + 25x + x2) = 0

Factor a trinomial.
4((-28 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
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

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 = {-28, 3}

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