(6x+20)(x-12)=(5x+18)(x-13)

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Solution for (6x+20)(x-12)=(5x+18)(x-13) equation: 


Simplifying
(6x + 20)(x + -12) = (5x + 18)(x + -13)

Reorder the terms:
(20 + 6x)(x + -12) = (5x + 18)(x + -13)

Reorder the terms:
(20 + 6x)(-12 + x) = (5x + 18)(x + -13)

Multiply (20 + 6x) * (-12 + x)
(20(-12 + x) + 6x * (-12 + x)) = (5x + 18)(x + -13)
((-12 * 20 + x * 20) + 6x * (-12 + x)) = (5x + 18)(x + -13)
((-240 + 20x) + 6x * (-12 + x)) = (5x + 18)(x + -13)
(-240 + 20x + (-12 * 6x + x * 6x)) = (5x + 18)(x + -13)
(-240 + 20x + (-72x + 6x2)) = (5x + 18)(x + -13)

Combine like terms: 20x + -72x = -52x
(-240 + -52x + 6x2) = (5x + 18)(x + -13)

Reorder the terms:
-240 + -52x + 6x2 = (18 + 5x)(x + -13)

Reorder the terms:
-240 + -52x + 6x2 = (18 + 5x)(-13 + x)

Multiply (18 + 5x) * (-13 + x)
-240 + -52x + 6x2 = (18(-13 + x) + 5x * (-13 + x))
-240 + -52x + 6x2 = ((-13 * 18 + x * 18) + 5x * (-13 + x))
-240 + -52x + 6x2 = ((-234 + 18x) + 5x * (-13 + x))
-240 + -52x + 6x2 = (-234 + 18x + (-13 * 5x + x * 5x))
-240 + -52x + 6x2 = (-234 + 18x + (-65x + 5x2))

Combine like terms: 18x + -65x = -47x
-240 + -52x + 6x2 = (-234 + -47x + 5x2)

Solving
-240 + -52x + 6x2 = -234 + -47x + 5x2

Solving for variable 'x'.

Reorder the terms:
-240 + 234 + -52x + 47x + 6x2 + -5x2 = -234 + -47x + 5x2 + 234 + 47x + -5x2

Combine like terms: -240 + 234 = -6
-6 + -52x + 47x + 6x2 + -5x2 = -234 + -47x + 5x2 + 234 + 47x + -5x2

Combine like terms: -52x + 47x = -5x
-6 + -5x + 6x2 + -5x2 = -234 + -47x + 5x2 + 234 + 47x + -5x2

Combine like terms: 6x2 + -5x2 = 1x2
-6 + -5x + 1x2 = -234 + -47x + 5x2 + 234 + 47x + -5x2

Reorder the terms:
-6 + -5x + 1x2 = -234 + 234 + -47x + 47x + 5x2 + -5x2

Combine like terms: -234 + 234 = 0
-6 + -5x + 1x2 = 0 + -47x + 47x + 5x2 + -5x2
-6 + -5x + 1x2 = -47x + 47x + 5x2 + -5x2

Combine like terms: -47x + 47x = 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.
(-1 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-1, 6}

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