(2x-5)(x-7)=(x-7)(4-11x)

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Solution for (2x-5)(x-7)=(x-7)(4-11x) equation:


Simplifying
(2x + -5)(x + -7) = (x + -7)(4 + -11x)

Reorder the terms:
(-5 + 2x)(x + -7) = (x + -7)(4 + -11x)

Reorder the terms:
(-5 + 2x)(-7 + x) = (x + -7)(4 + -11x)

Multiply (-5 + 2x) * (-7 + x)
(-5(-7 + x) + 2x * (-7 + x)) = (x + -7)(4 + -11x)
((-7 * -5 + x * -5) + 2x * (-7 + x)) = (x + -7)(4 + -11x)
((35 + -5x) + 2x * (-7 + x)) = (x + -7)(4 + -11x)
(35 + -5x + (-7 * 2x + x * 2x)) = (x + -7)(4 + -11x)
(35 + -5x + (-14x + 2x2)) = (x + -7)(4 + -11x)

Combine like terms: -5x + -14x = -19x
(35 + -19x + 2x2) = (x + -7)(4 + -11x)

Reorder the terms:
35 + -19x + 2x2 = (-7 + x)(4 + -11x)

Multiply (-7 + x) * (4 + -11x)
35 + -19x + 2x2 = (-7(4 + -11x) + x(4 + -11x))
35 + -19x + 2x2 = ((4 * -7 + -11x * -7) + x(4 + -11x))
35 + -19x + 2x2 = ((-28 + 77x) + x(4 + -11x))
35 + -19x + 2x2 = (-28 + 77x + (4 * x + -11x * x))
35 + -19x + 2x2 = (-28 + 77x + (4x + -11x2))

Combine like terms: 77x + 4x = 81x
35 + -19x + 2x2 = (-28 + 81x + -11x2)

Solving
35 + -19x + 2x2 = -28 + 81x + -11x2

Solving for variable 'x'.

Reorder the terms:
35 + 28 + -19x + -81x + 2x2 + 11x2 = -28 + 81x + -11x2 + 28 + -81x + 11x2

Combine like terms: 35 + 28 = 63
63 + -19x + -81x + 2x2 + 11x2 = -28 + 81x + -11x2 + 28 + -81x + 11x2

Combine like terms: -19x + -81x = -100x
63 + -100x + 2x2 + 11x2 = -28 + 81x + -11x2 + 28 + -81x + 11x2

Combine like terms: 2x2 + 11x2 = 13x2
63 + -100x + 13x2 = -28 + 81x + -11x2 + 28 + -81x + 11x2

Reorder the terms:
63 + -100x + 13x2 = -28 + 28 + 81x + -81x + -11x2 + 11x2

Combine like terms: -28 + 28 = 0
63 + -100x + 13x2 = 0 + 81x + -81x + -11x2 + 11x2
63 + -100x + 13x2 = 81x + -81x + -11x2 + 11x2

Combine like terms: 81x + -81x = 0
63 + -100x + 13x2 = 0 + -11x2 + 11x2
63 + -100x + 13x2 = -11x2 + 11x2

Combine like terms: -11x2 + 11x2 = 0
63 + -100x + 13x2 = 0

Factor a trinomial.
(9 + -13x)(7 + -1x) = 0


Subproblem 1
Set the factor '(9 + -13x)' equal to zero and attempt to solve:

Simplifying
9 + -13x = 0

Solving
9 + -13x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -13x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -13x = 0 + -9
-13x = 0 + -9

Combine like terms: 0 + -9 = -9
-13x = -9

Divide each side by '-13'.
x = 0.6923076923

Simplifying
x = 0.6923076923

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 = {0.6923076923, 7}

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