(x-5)(x-5)=(x-6)(x-3)

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Solution for (x-5)(x-5)=(x-6)(x-3) equation: 


Simplifying
(x + -5)(x + -5) = (x + -6)(x + -3)

Reorder the terms:
(-5 + x)(x + -5) = (x + -6)(x + -3)

Reorder the terms:
(-5 + x)(-5 + x) = (x + -6)(x + -3)

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) = (x + -6)(x + -3)
((-5 * -5 + x * -5) + x(-5 + x)) = (x + -6)(x + -3)
((25 + -5x) + x(-5 + x)) = (x + -6)(x + -3)
(25 + -5x + (-5 * x + x * x)) = (x + -6)(x + -3)
(25 + -5x + (-5x + x2)) = (x + -6)(x + -3)

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) = (x + -6)(x + -3)

Reorder the terms:
25 + -10x + x2 = (-6 + x)(x + -3)

Reorder the terms:
25 + -10x + x2 = (-6 + x)(-3 + x)

Multiply (-6 + x) * (-3 + x)
25 + -10x + x2 = (-6(-3 + x) + x(-3 + x))
25 + -10x + x2 = ((-3 * -6 + x * -6) + x(-3 + x))
25 + -10x + x2 = ((18 + -6x) + x(-3 + x))
25 + -10x + x2 = (18 + -6x + (-3 * x + x * x))
25 + -10x + x2 = (18 + -6x + (-3x + x2))

Combine like terms: -6x + -3x = -9x
25 + -10x + x2 = (18 + -9x + x2)

Add '-1x2' to each side of the equation.
25 + -10x + x2 + -1x2 = 18 + -9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
25 + -10x + 0 = 18 + -9x + x2 + -1x2
25 + -10x = 18 + -9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
25 + -10x = 18 + -9x + 0
25 + -10x = 18 + -9x

Solving
25 + -10x = 18 + -9x

Solving for variable 'x'.

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

Add '9x' to each side of the equation.
25 + -10x + 9x = 18 + -9x + 9x

Combine like terms: -10x + 9x = -1x
25 + -1x = 18 + -9x + 9x

Combine like terms: -9x + 9x = 0
25 + -1x = 18 + 0
25 + -1x = 18

Add '-25' to each side of the equation.
25 + -25 + -1x = 18 + -25

Combine like terms: 25 + -25 = 0
0 + -1x = 18 + -25
-1x = 18 + -25

Combine like terms: 18 + -25 = -7
-1x = -7

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

Simplifying
x = 7

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