378=(32+2x)(29+2x)

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Solution for 378=(32+2x)(29+2x) equation: 


Simplifying
378 = (32 + 2x)(29 + 2x)

Multiply (32 + 2x) * (29 + 2x)
378 = (32(29 + 2x) + 2x * (29 + 2x))
378 = ((29 * 32 + 2x * 32) + 2x * (29 + 2x))
378 = ((928 + 64x) + 2x * (29 + 2x))
378 = (928 + 64x + (29 * 2x + 2x * 2x))
378 = (928 + 64x + (58x + 4x2))

Combine like terms: 64x + 58x = 122x
378 = (928 + 122x + 4x2)

Solving
378 = 928 + 122x + 4x2

Solving for variable 'x'.

Combine like terms: 378 + -928 = -550
-550 + -122x + -4x2 = 928 + 122x + 4x2 + -928 + -122x + -4x2

Reorder the terms:
-550 + -122x + -4x2 = 928 + -928 + 122x + -122x + 4x2 + -4x2

Combine like terms: 928 + -928 = 0
-550 + -122x + -4x2 = 0 + 122x + -122x + 4x2 + -4x2
-550 + -122x + -4x2 = 122x + -122x + 4x2 + -4x2

Combine like terms: 122x + -122x = 0
-550 + -122x + -4x2 = 0 + 4x2 + -4x2
-550 + -122x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-550 + -122x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(275 + 61x + 2x2) = 0

Factor a trinomial.
-2((25 + x)(11 + 2x)) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(25 + x)' equal to zero and attempt to solve:

Simplifying
25 + x = 0

Solving
25 + x = 0

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

Add '-25' to each side of the equation.
25 + -25 + x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + x = 0 + -25
x = 0 + -25

Combine like terms: 0 + -25 = -25
x = -25

Simplifying
x = -25

Subproblem 2
Set the factor '(11 + 2x)' equal to zero and attempt to solve:

Simplifying
11 + 2x = 0

Solving
11 + 2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2x = 0 + -11
2x = 0 + -11

Combine like terms: 0 + -11 = -11
2x = -11

Divide each side by '2'.
x = -5.5

Simplifying
x = -5.5
Solution
x = {-25, -5.5}

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