(6x-7)(x-9)=(1-4x)(x+3)

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Solution for (6x-7)(x-9)=(1-4x)(x+3) equation: 


Simplifying
(6x + -7)(x + -9) = (1 + -4x)(x + 3)

Reorder the terms:
(-7 + 6x)(x + -9) = (1 + -4x)(x + 3)

Reorder the terms:
(-7 + 6x)(-9 + x) = (1 + -4x)(x + 3)

Multiply (-7 + 6x) * (-9 + x)
(-7(-9 + x) + 6x * (-9 + x)) = (1 + -4x)(x + 3)
((-9 * -7 + x * -7) + 6x * (-9 + x)) = (1 + -4x)(x + 3)
((63 + -7x) + 6x * (-9 + x)) = (1 + -4x)(x + 3)
(63 + -7x + (-9 * 6x + x * 6x)) = (1 + -4x)(x + 3)
(63 + -7x + (-54x + 6x2)) = (1 + -4x)(x + 3)

Combine like terms: -7x + -54x = -61x
(63 + -61x + 6x2) = (1 + -4x)(x + 3)

Reorder the terms:
63 + -61x + 6x2 = (1 + -4x)(3 + x)

Multiply (1 + -4x) * (3 + x)
63 + -61x + 6x2 = (1(3 + x) + -4x * (3 + x))
63 + -61x + 6x2 = ((3 * 1 + x * 1) + -4x * (3 + x))
63 + -61x + 6x2 = ((3 + 1x) + -4x * (3 + x))
63 + -61x + 6x2 = (3 + 1x + (3 * -4x + x * -4x))
63 + -61x + 6x2 = (3 + 1x + (-12x + -4x2))

Combine like terms: 1x + -12x = -11x
63 + -61x + 6x2 = (3 + -11x + -4x2)

Solving
63 + -61x + 6x2 = 3 + -11x + -4x2

Solving for variable 'x'.

Reorder the terms:
63 + -3 + -61x + 11x + 6x2 + 4x2 = 3 + -11x + -4x2 + -3 + 11x + 4x2

Combine like terms: 63 + -3 = 60
60 + -61x + 11x + 6x2 + 4x2 = 3 + -11x + -4x2 + -3 + 11x + 4x2

Combine like terms: -61x + 11x = -50x
60 + -50x + 6x2 + 4x2 = 3 + -11x + -4x2 + -3 + 11x + 4x2

Combine like terms: 6x2 + 4x2 = 10x2
60 + -50x + 10x2 = 3 + -11x + -4x2 + -3 + 11x + 4x2

Reorder the terms:
60 + -50x + 10x2 = 3 + -3 + -11x + 11x + -4x2 + 4x2

Combine like terms: 3 + -3 = 0
60 + -50x + 10x2 = 0 + -11x + 11x + -4x2 + 4x2
60 + -50x + 10x2 = -11x + 11x + -4x2 + 4x2

Combine like terms: -11x + 11x = 0
60 + -50x + 10x2 = 0 + -4x2 + 4x2
60 + -50x + 10x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
60 + -50x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(6 + -5x + x2) = 0

Factor a trinomial.
10((2 + -1x)(3 + -1x)) = 0

Ignore the factor 10.

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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