(4x-3)(x+9)=(x-13)(1-3x)

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Solution for (4x-3)(x+9)=(x-13)(1-3x) equation: 


Simplifying
(4x + -3)(x + 9) = (x + -13)(1 + -3x)

Reorder the terms:
(-3 + 4x)(x + 9) = (x + -13)(1 + -3x)

Reorder the terms:
(-3 + 4x)(9 + x) = (x + -13)(1 + -3x)

Multiply (-3 + 4x) * (9 + x)
(-3(9 + x) + 4x * (9 + x)) = (x + -13)(1 + -3x)
((9 * -3 + x * -3) + 4x * (9 + x)) = (x + -13)(1 + -3x)
((-27 + -3x) + 4x * (9 + x)) = (x + -13)(1 + -3x)
(-27 + -3x + (9 * 4x + x * 4x)) = (x + -13)(1 + -3x)
(-27 + -3x + (36x + 4x2)) = (x + -13)(1 + -3x)

Combine like terms: -3x + 36x = 33x
(-27 + 33x + 4x2) = (x + -13)(1 + -3x)

Reorder the terms:
-27 + 33x + 4x2 = (-13 + x)(1 + -3x)

Multiply (-13 + x) * (1 + -3x)
-27 + 33x + 4x2 = (-13(1 + -3x) + x(1 + -3x))
-27 + 33x + 4x2 = ((1 * -13 + -3x * -13) + x(1 + -3x))
-27 + 33x + 4x2 = ((-13 + 39x) + x(1 + -3x))
-27 + 33x + 4x2 = (-13 + 39x + (1 * x + -3x * x))
-27 + 33x + 4x2 = (-13 + 39x + (1x + -3x2))

Combine like terms: 39x + 1x = 40x
-27 + 33x + 4x2 = (-13 + 40x + -3x2)

Solving
-27 + 33x + 4x2 = -13 + 40x + -3x2

Solving for variable 'x'.

Reorder the terms:
-27 + 13 + 33x + -40x + 4x2 + 3x2 = -13 + 40x + -3x2 + 13 + -40x + 3x2

Combine like terms: -27 + 13 = -14
-14 + 33x + -40x + 4x2 + 3x2 = -13 + 40x + -3x2 + 13 + -40x + 3x2

Combine like terms: 33x + -40x = -7x
-14 + -7x + 4x2 + 3x2 = -13 + 40x + -3x2 + 13 + -40x + 3x2

Combine like terms: 4x2 + 3x2 = 7x2
-14 + -7x + 7x2 = -13 + 40x + -3x2 + 13 + -40x + 3x2

Reorder the terms:
-14 + -7x + 7x2 = -13 + 13 + 40x + -40x + -3x2 + 3x2

Combine like terms: -13 + 13 = 0
-14 + -7x + 7x2 = 0 + 40x + -40x + -3x2 + 3x2
-14 + -7x + 7x2 = 40x + -40x + -3x2 + 3x2

Combine like terms: 40x + -40x = 0
-14 + -7x + 7x2 = 0 + -3x2 + 3x2
-14 + -7x + 7x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-14 + -7x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-2 + -1x + x2) = 0

Factor a trinomial.
7((-1 + -1x)(2 + -1x)) = 0

Ignore the factor 7.

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 '(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
Solution
x = {-1, 2}

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