(2c-1)(c-5)+(a-4)(c-3)=

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Solution for (2c-1)(c-5)+(a-4)(c-3)= equation: 


Simplifying
(2c + -1)(c + -5) + (a + -4)(c + -3) = 0

Reorder the terms:
(-1 + 2c)(c + -5) + (a + -4)(c + -3) = 0

Reorder the terms:
(-1 + 2c)(-5 + c) + (a + -4)(c + -3) = 0

Multiply (-1 + 2c) * (-5 + c)
(-1(-5 + c) + 2c * (-5 + c)) + (a + -4)(c + -3) = 0
((-5 * -1 + c * -1) + 2c * (-5 + c)) + (a + -4)(c + -3) = 0
((5 + -1c) + 2c * (-5 + c)) + (a + -4)(c + -3) = 0
(5 + -1c + (-5 * 2c + c * 2c)) + (a + -4)(c + -3) = 0
(5 + -1c + (-10c + 2c2)) + (a + -4)(c + -3) = 0

Combine like terms: -1c + -10c = -11c
(5 + -11c + 2c2) + (a + -4)(c + -3) = 0

Reorder the terms:
5 + -11c + 2c2 + (-4 + a)(c + -3) = 0

Reorder the terms:
5 + -11c + 2c2 + (-4 + a)(-3 + c) = 0

Multiply (-4 + a) * (-3 + c)
5 + -11c + 2c2 + (-4(-3 + c) + a(-3 + c)) = 0
5 + -11c + 2c2 + ((-3 * -4 + c * -4) + a(-3 + c)) = 0
5 + -11c + 2c2 + ((12 + -4c) + a(-3 + c)) = 0
5 + -11c + 2c2 + (12 + -4c + (-3 * a + c * a)) = 0
5 + -11c + 2c2 + (12 + -4c + (-3a + ac)) = 0

Reorder the terms:
5 + -11c + 2c2 + (12 + -3a + ac + -4c) = 0
5 + -11c + 2c2 + (12 + -3a + ac + -4c) = 0

Reorder the terms:
5 + 12 + -3a + ac + -11c + -4c + 2c2 = 0

Combine like terms: 5 + 12 = 17
17 + -3a + ac + -11c + -4c + 2c2 = 0

Combine like terms: -11c + -4c = -15c
17 + -3a + ac + -15c + 2c2 = 0

Solving
17 + -3a + ac + -15c + 2c2 = 0

Solving for variable 'a'.

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

Add '-17' to each side of the equation.
17 + -3a + ac + -15c + -17 + 2c2 = 0 + -17

Reorder the terms:
17 + -17 + -3a + ac + -15c + 2c2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -3a + ac + -15c + 2c2 = 0 + -17
-3a + ac + -15c + 2c2 = 0 + -17

Combine like terms: 0 + -17 = -17
-3a + ac + -15c + 2c2 = -17

Add '15c' to each side of the equation.
-3a + ac + -15c + 15c + 2c2 = -17 + 15c

Combine like terms: -15c + 15c = 0
-3a + ac + 0 + 2c2 = -17 + 15c
-3a + ac + 2c2 = -17 + 15c

Add '-2c2' to each side of the equation.
-3a + ac + 2c2 + -2c2 = -17 + 15c + -2c2

Combine like terms: 2c2 + -2c2 = 0
-3a + ac + 0 = -17 + 15c + -2c2
-3a + ac = -17 + 15c + -2c2

Reorder the terms:
17 + -3a + ac + -15c + 2c2 = -17 + 15c + -2c2 + 17 + -15c + 2c2

Reorder the terms:
17 + -3a + ac + -15c + 2c2 = -17 + 17 + 15c + -15c + -2c2 + 2c2

Combine like terms: -17 + 17 = 0
17 + -3a + ac + -15c + 2c2 = 0 + 15c + -15c + -2c2 + 2c2
17 + -3a + ac + -15c + 2c2 = 15c + -15c + -2c2 + 2c2

Combine like terms: 15c + -15c = 0
17 + -3a + ac + -15c + 2c2 = 0 + -2c2 + 2c2
17 + -3a + ac + -15c + 2c2 = -2c2 + 2c2

Combine like terms: -2c2 + 2c2 = 0
17 + -3a + ac + -15c + 2c2 = 0

The solution to this equation could not be determined.

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