(4x-3)(x+7)=(x-9)(1-2x)

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Solution for (4x-3)(x+7)=(x-9)(1-2x) equation: 


Simplifying
(4x + -3)(x + 7) = (x + -9)(1 + -2x)

Reorder the terms:
(-3 + 4x)(x + 7) = (x + -9)(1 + -2x)

Reorder the terms:
(-3 + 4x)(7 + x) = (x + -9)(1 + -2x)

Multiply (-3 + 4x) * (7 + x)
(-3(7 + x) + 4x * (7 + x)) = (x + -9)(1 + -2x)
((7 * -3 + x * -3) + 4x * (7 + x)) = (x + -9)(1 + -2x)
((-21 + -3x) + 4x * (7 + x)) = (x + -9)(1 + -2x)
(-21 + -3x + (7 * 4x + x * 4x)) = (x + -9)(1 + -2x)
(-21 + -3x + (28x + 4x2)) = (x + -9)(1 + -2x)

Combine like terms: -3x + 28x = 25x
(-21 + 25x + 4x2) = (x + -9)(1 + -2x)

Reorder the terms:
-21 + 25x + 4x2 = (-9 + x)(1 + -2x)

Multiply (-9 + x) * (1 + -2x)
-21 + 25x + 4x2 = (-9(1 + -2x) + x(1 + -2x))
-21 + 25x + 4x2 = ((1 * -9 + -2x * -9) + x(1 + -2x))
-21 + 25x + 4x2 = ((-9 + 18x) + x(1 + -2x))
-21 + 25x + 4x2 = (-9 + 18x + (1 * x + -2x * x))
-21 + 25x + 4x2 = (-9 + 18x + (1x + -2x2))

Combine like terms: 18x + 1x = 19x
-21 + 25x + 4x2 = (-9 + 19x + -2x2)

Solving
-21 + 25x + 4x2 = -9 + 19x + -2x2

Solving for variable 'x'.

Reorder the terms:
-21 + 9 + 25x + -19x + 4x2 + 2x2 = -9 + 19x + -2x2 + 9 + -19x + 2x2

Combine like terms: -21 + 9 = -12
-12 + 25x + -19x + 4x2 + 2x2 = -9 + 19x + -2x2 + 9 + -19x + 2x2

Combine like terms: 25x + -19x = 6x
-12 + 6x + 4x2 + 2x2 = -9 + 19x + -2x2 + 9 + -19x + 2x2

Combine like terms: 4x2 + 2x2 = 6x2
-12 + 6x + 6x2 = -9 + 19x + -2x2 + 9 + -19x + 2x2

Reorder the terms:
-12 + 6x + 6x2 = -9 + 9 + 19x + -19x + -2x2 + 2x2

Combine like terms: -9 + 9 = 0
-12 + 6x + 6x2 = 0 + 19x + -19x + -2x2 + 2x2
-12 + 6x + 6x2 = 19x + -19x + -2x2 + 2x2

Combine like terms: 19x + -19x = 0
-12 + 6x + 6x2 = 0 + -2x2 + 2x2
-12 + 6x + 6x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-12 + 6x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + x + x2) = 0

Factor a trinomial.
6((-2 + -1x)(1 + -1x)) = 0

Ignore the factor 6.

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 '(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 = {-2, 1}

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