(12+2x)(15+2x)=460

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Solution for (12+2x)(15+2x)=460 equation: 


Simplifying
(12 + 2x)(15 + 2x) = 460

Multiply (12 + 2x) * (15 + 2x)
(12(15 + 2x) + 2x * (15 + 2x)) = 460
((15 * 12 + 2x * 12) + 2x * (15 + 2x)) = 460
((180 + 24x) + 2x * (15 + 2x)) = 460
(180 + 24x + (15 * 2x + 2x * 2x)) = 460
(180 + 24x + (30x + 4x2)) = 460

Combine like terms: 24x + 30x = 54x
(180 + 54x + 4x2) = 460

Solving
180 + 54x + 4x2 = 460

Solving for variable 'x'.

Reorder the terms:
180 + -460 + 54x + 4x2 = 460 + -460

Combine like terms: 180 + -460 = -280
-280 + 54x + 4x2 = 460 + -460

Combine like terms: 460 + -460 = 0
-280 + 54x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-140 + 27x + 2x2) = 0

Factor a trinomial.
2((-35 + -2x)(4 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-35 + -2x)' equal to zero and attempt to solve:

Simplifying
-35 + -2x = 0

Solving
-35 + -2x = 0

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

Add '35' to each side of the equation.
-35 + 35 + -2x = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -2x = 0 + 35
-2x = 0 + 35

Combine like terms: 0 + 35 = 35
-2x = 35

Divide each side by '-2'.
x = -17.5

Simplifying
x = -17.5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-17.5, 4}

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