(x-7)*(4x-1)-(7-2x)*(x-7)=0

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Solution for (x-7)*(4x-1)-(7-2x)*(x-7)=0 equation: 


Simplifying
(x + -7)(4x + -1) + -1(7 + -2x)(x + -7) = 0

Reorder the terms:
(-7 + x)(4x + -1) + -1(7 + -2x)(x + -7) = 0

Reorder the terms:
(-7 + x)(-1 + 4x) + -1(7 + -2x)(x + -7) = 0

Multiply (-7 + x) * (-1 + 4x)
(-7(-1 + 4x) + x(-1 + 4x)) + -1(7 + -2x)(x + -7) = 0
((-1 * -7 + 4x * -7) + x(-1 + 4x)) + -1(7 + -2x)(x + -7) = 0
((7 + -28x) + x(-1 + 4x)) + -1(7 + -2x)(x + -7) = 0
(7 + -28x + (-1 * x + 4x * x)) + -1(7 + -2x)(x + -7) = 0
(7 + -28x + (-1x + 4x2)) + -1(7 + -2x)(x + -7) = 0

Combine like terms: -28x + -1x = -29x
(7 + -29x + 4x2) + -1(7 + -2x)(x + -7) = 0

Reorder the terms:
7 + -29x + 4x2 + -1(7 + -2x)(-7 + x) = 0

Multiply (7 + -2x) * (-7 + x)
7 + -29x + 4x2 + -1(7(-7 + x) + -2x * (-7 + x)) = 0
7 + -29x + 4x2 + -1((-7 * 7 + x * 7) + -2x * (-7 + x)) = 0
7 + -29x + 4x2 + -1((-49 + 7x) + -2x * (-7 + x)) = 0
7 + -29x + 4x2 + -1(-49 + 7x + (-7 * -2x + x * -2x)) = 0
7 + -29x + 4x2 + -1(-49 + 7x + (14x + -2x2)) = 0

Combine like terms: 7x + 14x = 21x
7 + -29x + 4x2 + -1(-49 + 21x + -2x2) = 0
7 + -29x + 4x2 + (-49 * -1 + 21x * -1 + -2x2 * -1) = 0
7 + -29x + 4x2 + (49 + -21x + 2x2) = 0

Reorder the terms:
7 + 49 + -29x + -21x + 4x2 + 2x2 = 0

Combine like terms: 7 + 49 = 56
56 + -29x + -21x + 4x2 + 2x2 = 0

Combine like terms: -29x + -21x = -50x
56 + -50x + 4x2 + 2x2 = 0

Combine like terms: 4x2 + 2x2 = 6x2
56 + -50x + 6x2 = 0

Solving
56 + -50x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -25x + 3x2) = 0

Factor a trinomial.
2((4 + -3x)(7 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1.333333333, 7}

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