26(x-7)(x+5)=(x+5)(x-7)

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Solution for 26(x-7)(x+5)=(x+5)(x-7) equation: 


Simplifying
26(x + -7)(x + 5) = (x + 5)(x + -7)

Reorder the terms:
26(-7 + x)(x + 5) = (x + 5)(x + -7)

Reorder the terms:
26(-7 + x)(5 + x) = (x + 5)(x + -7)

Multiply (-7 + x) * (5 + x)
26(-7(5 + x) + x(5 + x)) = (x + 5)(x + -7)
26((5 * -7 + x * -7) + x(5 + x)) = (x + 5)(x + -7)
26((-35 + -7x) + x(5 + x)) = (x + 5)(x + -7)
26(-35 + -7x + (5 * x + x * x)) = (x + 5)(x + -7)
26(-35 + -7x + (5x + x2)) = (x + 5)(x + -7)

Combine like terms: -7x + 5x = -2x
26(-35 + -2x + x2) = (x + 5)(x + -7)
(-35 * 26 + -2x * 26 + x2 * 26) = (x + 5)(x + -7)
(-910 + -52x + 26x2) = (x + 5)(x + -7)

Reorder the terms:
-910 + -52x + 26x2 = (5 + x)(x + -7)

Reorder the terms:
-910 + -52x + 26x2 = (5 + x)(-7 + x)

Multiply (5 + x) * (-7 + x)
-910 + -52x + 26x2 = (5(-7 + x) + x(-7 + x))
-910 + -52x + 26x2 = ((-7 * 5 + x * 5) + x(-7 + x))
-910 + -52x + 26x2 = ((-35 + 5x) + x(-7 + x))
-910 + -52x + 26x2 = (-35 + 5x + (-7 * x + x * x))
-910 + -52x + 26x2 = (-35 + 5x + (-7x + x2))

Combine like terms: 5x + -7x = -2x
-910 + -52x + 26x2 = (-35 + -2x + x2)

Solving
-910 + -52x + 26x2 = -35 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-910 + 35 + -52x + 2x + 26x2 + -1x2 = -35 + -2x + x2 + 35 + 2x + -1x2

Combine like terms: -910 + 35 = -875
-875 + -52x + 2x + 26x2 + -1x2 = -35 + -2x + x2 + 35 + 2x + -1x2

Combine like terms: -52x + 2x = -50x
-875 + -50x + 26x2 + -1x2 = -35 + -2x + x2 + 35 + 2x + -1x2

Combine like terms: 26x2 + -1x2 = 25x2
-875 + -50x + 25x2 = -35 + -2x + x2 + 35 + 2x + -1x2

Reorder the terms:
-875 + -50x + 25x2 = -35 + 35 + -2x + 2x + x2 + -1x2

Combine like terms: -35 + 35 = 0
-875 + -50x + 25x2 = 0 + -2x + 2x + x2 + -1x2
-875 + -50x + 25x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
-875 + -50x + 25x2 = 0 + x2 + -1x2
-875 + -50x + 25x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-875 + -50x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '25'.
25(-35 + -2x + x2) = 0

Factor a trinomial.
25((-5 + -1x)(7 + -1x)) = 0

Ignore the factor 25.

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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 = {-5, 7}

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