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

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


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

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

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

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

Combine like terms: -1x + -8x = -9x
(2 + -9x + 4x2) = (3x + -7)(x + 2)

Reorder the terms:
2 + -9x + 4x2 = (-7 + 3x)(x + 2)

Reorder the terms:
2 + -9x + 4x2 = (-7 + 3x)(2 + x)

Multiply (-7 + 3x) * (2 + x)
2 + -9x + 4x2 = (-7(2 + x) + 3x * (2 + x))
2 + -9x + 4x2 = ((2 * -7 + x * -7) + 3x * (2 + x))
2 + -9x + 4x2 = ((-14 + -7x) + 3x * (2 + x))
2 + -9x + 4x2 = (-14 + -7x + (2 * 3x + x * 3x))
2 + -9x + 4x2 = (-14 + -7x + (6x + 3x2))

Combine like terms: -7x + 6x = -1x
2 + -9x + 4x2 = (-14 + -1x + 3x2)

Solving
2 + -9x + 4x2 = -14 + -1x + 3x2

Solving for variable 'x'.

Reorder the terms:
2 + 14 + -9x + x + 4x2 + -3x2 = -14 + -1x + 3x2 + 14 + x + -3x2

Combine like terms: 2 + 14 = 16
16 + -9x + x + 4x2 + -3x2 = -14 + -1x + 3x2 + 14 + x + -3x2

Combine like terms: -9x + x = -8x
16 + -8x + 4x2 + -3x2 = -14 + -1x + 3x2 + 14 + x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
16 + -8x + 1x2 = -14 + -1x + 3x2 + 14 + x + -3x2

Reorder the terms:
16 + -8x + 1x2 = -14 + 14 + -1x + x + 3x2 + -3x2

Combine like terms: -14 + 14 = 0
16 + -8x + 1x2 = 0 + -1x + x + 3x2 + -3x2
16 + -8x + 1x2 = -1x + x + 3x2 + -3x2

Combine like terms: -1x + x = 0
16 + -8x + 1x2 = 0 + 3x2 + -3x2
16 + -8x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
16 + -8x + 1x2 = 0

Factor a trinomial.
(4 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {4, 4}

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