(6x+30)(x-12)=(5x+28)(x-13)

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Solution for (6x+30)(x-12)=(5x+28)(x-13) equation: 


Simplifying
(6x + 30)(x + -12) = (5x + 28)(x + -13)

Reorder the terms:
(30 + 6x)(x + -12) = (5x + 28)(x + -13)

Reorder the terms:
(30 + 6x)(-12 + x) = (5x + 28)(x + -13)

Multiply (30 + 6x) * (-12 + x)
(30(-12 + x) + 6x * (-12 + x)) = (5x + 28)(x + -13)
((-12 * 30 + x * 30) + 6x * (-12 + x)) = (5x + 28)(x + -13)
((-360 + 30x) + 6x * (-12 + x)) = (5x + 28)(x + -13)
(-360 + 30x + (-12 * 6x + x * 6x)) = (5x + 28)(x + -13)
(-360 + 30x + (-72x + 6x2)) = (5x + 28)(x + -13)

Combine like terms: 30x + -72x = -42x
(-360 + -42x + 6x2) = (5x + 28)(x + -13)

Reorder the terms:
-360 + -42x + 6x2 = (28 + 5x)(x + -13)

Reorder the terms:
-360 + -42x + 6x2 = (28 + 5x)(-13 + x)

Multiply (28 + 5x) * (-13 + x)
-360 + -42x + 6x2 = (28(-13 + x) + 5x * (-13 + x))
-360 + -42x + 6x2 = ((-13 * 28 + x * 28) + 5x * (-13 + x))
-360 + -42x + 6x2 = ((-364 + 28x) + 5x * (-13 + x))
-360 + -42x + 6x2 = (-364 + 28x + (-13 * 5x + x * 5x))
-360 + -42x + 6x2 = (-364 + 28x + (-65x + 5x2))

Combine like terms: 28x + -65x = -37x
-360 + -42x + 6x2 = (-364 + -37x + 5x2)

Solving
-360 + -42x + 6x2 = -364 + -37x + 5x2

Solving for variable 'x'.

Reorder the terms:
-360 + 364 + -42x + 37x + 6x2 + -5x2 = -364 + -37x + 5x2 + 364 + 37x + -5x2

Combine like terms: -360 + 364 = 4
4 + -42x + 37x + 6x2 + -5x2 = -364 + -37x + 5x2 + 364 + 37x + -5x2

Combine like terms: -42x + 37x = -5x
4 + -5x + 6x2 + -5x2 = -364 + -37x + 5x2 + 364 + 37x + -5x2

Combine like terms: 6x2 + -5x2 = 1x2
4 + -5x + 1x2 = -364 + -37x + 5x2 + 364 + 37x + -5x2

Reorder the terms:
4 + -5x + 1x2 = -364 + 364 + -37x + 37x + 5x2 + -5x2

Combine like terms: -364 + 364 = 0
4 + -5x + 1x2 = 0 + -37x + 37x + 5x2 + -5x2
4 + -5x + 1x2 = -37x + 37x + 5x2 + -5x2

Combine like terms: -37x + 37x = 0
4 + -5x + 1x2 = 0 + 5x2 + -5x2
4 + -5x + 1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
4 + -5x + 1x2 = 0

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


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

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 = {1, 4}

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