(3x-4)(x+7)=(x-13)(1-2x)

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Solution for (3x-4)(x+7)=(x-13)(1-2x) equation: 


Simplifying
(3x + -4)(x + 7) = (x + -13)(1 + -2x)

Reorder the terms:
(-4 + 3x)(x + 7) = (x + -13)(1 + -2x)

Reorder the terms:
(-4 + 3x)(7 + x) = (x + -13)(1 + -2x)

Multiply (-4 + 3x) * (7 + x)
(-4(7 + x) + 3x * (7 + x)) = (x + -13)(1 + -2x)
((7 * -4 + x * -4) + 3x * (7 + x)) = (x + -13)(1 + -2x)
((-28 + -4x) + 3x * (7 + x)) = (x + -13)(1 + -2x)
(-28 + -4x + (7 * 3x + x * 3x)) = (x + -13)(1 + -2x)
(-28 + -4x + (21x + 3x2)) = (x + -13)(1 + -2x)

Combine like terms: -4x + 21x = 17x
(-28 + 17x + 3x2) = (x + -13)(1 + -2x)

Reorder the terms:
-28 + 17x + 3x2 = (-13 + x)(1 + -2x)

Multiply (-13 + x) * (1 + -2x)
-28 + 17x + 3x2 = (-13(1 + -2x) + x(1 + -2x))
-28 + 17x + 3x2 = ((1 * -13 + -2x * -13) + x(1 + -2x))
-28 + 17x + 3x2 = ((-13 + 26x) + x(1 + -2x))
-28 + 17x + 3x2 = (-13 + 26x + (1 * x + -2x * x))
-28 + 17x + 3x2 = (-13 + 26x + (1x + -2x2))

Combine like terms: 26x + 1x = 27x
-28 + 17x + 3x2 = (-13 + 27x + -2x2)

Solving
-28 + 17x + 3x2 = -13 + 27x + -2x2

Solving for variable 'x'.

Reorder the terms:
-28 + 13 + 17x + -27x + 3x2 + 2x2 = -13 + 27x + -2x2 + 13 + -27x + 2x2

Combine like terms: -28 + 13 = -15
-15 + 17x + -27x + 3x2 + 2x2 = -13 + 27x + -2x2 + 13 + -27x + 2x2

Combine like terms: 17x + -27x = -10x
-15 + -10x + 3x2 + 2x2 = -13 + 27x + -2x2 + 13 + -27x + 2x2

Combine like terms: 3x2 + 2x2 = 5x2
-15 + -10x + 5x2 = -13 + 27x + -2x2 + 13 + -27x + 2x2

Reorder the terms:
-15 + -10x + 5x2 = -13 + 13 + 27x + -27x + -2x2 + 2x2

Combine like terms: -13 + 13 = 0
-15 + -10x + 5x2 = 0 + 27x + -27x + -2x2 + 2x2
-15 + -10x + 5x2 = 27x + -27x + -2x2 + 2x2

Combine like terms: 27x + -27x = 0
-15 + -10x + 5x2 = 0 + -2x2 + 2x2
-15 + -10x + 5x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-15 + -10x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -2x + x2) = 0

Factor a trinomial.
5((-1 + -1x)(3 + -1x)) = 0

Ignore the factor 5.

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 '(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 = {-1, 3}

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