(5x-7)(x+3)=(1-2x)(9-x)

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Solution for (5x-7)(x+3)=(1-2x)(9-x) equation: 


Simplifying
(5x + -7)(x + 3) = (1 + -2x)(9 + -1x)

Reorder the terms:
(-7 + 5x)(x + 3) = (1 + -2x)(9 + -1x)

Reorder the terms:
(-7 + 5x)(3 + x) = (1 + -2x)(9 + -1x)

Multiply (-7 + 5x) * (3 + x)
(-7(3 + x) + 5x * (3 + x)) = (1 + -2x)(9 + -1x)
((3 * -7 + x * -7) + 5x * (3 + x)) = (1 + -2x)(9 + -1x)
((-21 + -7x) + 5x * (3 + x)) = (1 + -2x)(9 + -1x)
(-21 + -7x + (3 * 5x + x * 5x)) = (1 + -2x)(9 + -1x)
(-21 + -7x + (15x + 5x2)) = (1 + -2x)(9 + -1x)

Combine like terms: -7x + 15x = 8x
(-21 + 8x + 5x2) = (1 + -2x)(9 + -1x)

Multiply (1 + -2x) * (9 + -1x)
-21 + 8x + 5x2 = (1(9 + -1x) + -2x * (9 + -1x))
-21 + 8x + 5x2 = ((9 * 1 + -1x * 1) + -2x * (9 + -1x))
-21 + 8x + 5x2 = ((9 + -1x) + -2x * (9 + -1x))
-21 + 8x + 5x2 = (9 + -1x + (9 * -2x + -1x * -2x))
-21 + 8x + 5x2 = (9 + -1x + (-18x + 2x2))

Combine like terms: -1x + -18x = -19x
-21 + 8x + 5x2 = (9 + -19x + 2x2)

Solving
-21 + 8x + 5x2 = 9 + -19x + 2x2

Solving for variable 'x'.

Reorder the terms:
-21 + -9 + 8x + 19x + 5x2 + -2x2 = 9 + -19x + 2x2 + -9 + 19x + -2x2

Combine like terms: -21 + -9 = -30
-30 + 8x + 19x + 5x2 + -2x2 = 9 + -19x + 2x2 + -9 + 19x + -2x2

Combine like terms: 8x + 19x = 27x
-30 + 27x + 5x2 + -2x2 = 9 + -19x + 2x2 + -9 + 19x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-30 + 27x + 3x2 = 9 + -19x + 2x2 + -9 + 19x + -2x2

Reorder the terms:
-30 + 27x + 3x2 = 9 + -9 + -19x + 19x + 2x2 + -2x2

Combine like terms: 9 + -9 = 0
-30 + 27x + 3x2 = 0 + -19x + 19x + 2x2 + -2x2
-30 + 27x + 3x2 = -19x + 19x + 2x2 + -2x2

Combine like terms: -19x + 19x = 0
-30 + 27x + 3x2 = 0 + 2x2 + -2x2
-30 + 27x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-30 + 27x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 9x + x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

Subproblem 2
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
Solution
x = {-10, 1}

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