(6x+32)(x-12)=(5x+30)(x-13)

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Solution for (6x+32)(x-12)=(5x+30)(x-13) equation: 


Simplifying
(6x + 32)(x + -12) = (5x + 30)(x + -13)

Reorder the terms:
(32 + 6x)(x + -12) = (5x + 30)(x + -13)

Reorder the terms:
(32 + 6x)(-12 + x) = (5x + 30)(x + -13)

Multiply (32 + 6x) * (-12 + x)
(32(-12 + x) + 6x * (-12 + x)) = (5x + 30)(x + -13)
((-12 * 32 + x * 32) + 6x * (-12 + x)) = (5x + 30)(x + -13)
((-384 + 32x) + 6x * (-12 + x)) = (5x + 30)(x + -13)
(-384 + 32x + (-12 * 6x + x * 6x)) = (5x + 30)(x + -13)
(-384 + 32x + (-72x + 6x2)) = (5x + 30)(x + -13)

Combine like terms: 32x + -72x = -40x
(-384 + -40x + 6x2) = (5x + 30)(x + -13)

Reorder the terms:
-384 + -40x + 6x2 = (30 + 5x)(x + -13)

Reorder the terms:
-384 + -40x + 6x2 = (30 + 5x)(-13 + x)

Multiply (30 + 5x) * (-13 + x)
-384 + -40x + 6x2 = (30(-13 + x) + 5x * (-13 + x))
-384 + -40x + 6x2 = ((-13 * 30 + x * 30) + 5x * (-13 + x))
-384 + -40x + 6x2 = ((-390 + 30x) + 5x * (-13 + x))
-384 + -40x + 6x2 = (-390 + 30x + (-13 * 5x + x * 5x))
-384 + -40x + 6x2 = (-390 + 30x + (-65x + 5x2))

Combine like terms: 30x + -65x = -35x
-384 + -40x + 6x2 = (-390 + -35x + 5x2)

Solving
-384 + -40x + 6x2 = -390 + -35x + 5x2

Solving for variable 'x'.

Reorder the terms:
-384 + 390 + -40x + 35x + 6x2 + -5x2 = -390 + -35x + 5x2 + 390 + 35x + -5x2

Combine like terms: -384 + 390 = 6
6 + -40x + 35x + 6x2 + -5x2 = -390 + -35x + 5x2 + 390 + 35x + -5x2

Combine like terms: -40x + 35x = -5x
6 + -5x + 6x2 + -5x2 = -390 + -35x + 5x2 + 390 + 35x + -5x2

Combine like terms: 6x2 + -5x2 = 1x2
6 + -5x + 1x2 = -390 + -35x + 5x2 + 390 + 35x + -5x2

Reorder the terms:
6 + -5x + 1x2 = -390 + 390 + -35x + 35x + 5x2 + -5x2

Combine like terms: -390 + 390 = 0
6 + -5x + 1x2 = 0 + -35x + 35x + 5x2 + -5x2
6 + -5x + 1x2 = -35x + 35x + 5x2 + -5x2

Combine like terms: -35x + 35x = 0
6 + -5x + 1x2 = 0 + 5x2 + -5x2
6 + -5x + 1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
6 + -5x + 1x2 = 0

Factor a trinomial.
(2 + -1x)(3 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, 3}

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