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

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


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

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

Multiply (-3 + 4x) * (1 + -2x)
(-3(1 + -2x) + 4x * (1 + -2x)) = (x + -9)(x + 7)
((1 * -3 + -2x * -3) + 4x * (1 + -2x)) = (x + -9)(x + 7)
((-3 + 6x) + 4x * (1 + -2x)) = (x + -9)(x + 7)
(-3 + 6x + (1 * 4x + -2x * 4x)) = (x + -9)(x + 7)
(-3 + 6x + (4x + -8x2)) = (x + -9)(x + 7)

Combine like terms: 6x + 4x = 10x
(-3 + 10x + -8x2) = (x + -9)(x + 7)

Reorder the terms:
-3 + 10x + -8x2 = (-9 + x)(x + 7)

Reorder the terms:
-3 + 10x + -8x2 = (-9 + x)(7 + x)

Multiply (-9 + x) * (7 + x)
-3 + 10x + -8x2 = (-9(7 + x) + x(7 + x))
-3 + 10x + -8x2 = ((7 * -9 + x * -9) + x(7 + x))
-3 + 10x + -8x2 = ((-63 + -9x) + x(7 + x))
-3 + 10x + -8x2 = (-63 + -9x + (7 * x + x * x))
-3 + 10x + -8x2 = (-63 + -9x + (7x + x2))

Combine like terms: -9x + 7x = -2x
-3 + 10x + -8x2 = (-63 + -2x + x2)

Solving
-3 + 10x + -8x2 = -63 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-3 + 63 + 10x + 2x + -8x2 + -1x2 = -63 + -2x + x2 + 63 + 2x + -1x2

Combine like terms: -3 + 63 = 60
60 + 10x + 2x + -8x2 + -1x2 = -63 + -2x + x2 + 63 + 2x + -1x2

Combine like terms: 10x + 2x = 12x
60 + 12x + -8x2 + -1x2 = -63 + -2x + x2 + 63 + 2x + -1x2

Combine like terms: -8x2 + -1x2 = -9x2
60 + 12x + -9x2 = -63 + -2x + x2 + 63 + 2x + -1x2

Reorder the terms:
60 + 12x + -9x2 = -63 + 63 + -2x + 2x + x2 + -1x2

Combine like terms: -63 + 63 = 0
60 + 12x + -9x2 = 0 + -2x + 2x + x2 + -1x2
60 + 12x + -9x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
60 + 12x + -9x2 = 0 + x2 + -1x2
60 + 12x + -9x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
60 + 12x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + 4x + -3x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 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 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {3.333333333, -2}

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