(c-2)(c-7)+(2c+7)(c-4)=c(2c-9)+96

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Solution for (c-2)(c-7)+(2c+7)(c-4)=c(2c-9)+96 equation:


Simplifying
(c + -2)(c + -7) + (2c + 7)(c + -4) = c(2c + -9) + 96

Reorder the terms:
(-2 + c)(c + -7) + (2c + 7)(c + -4) = c(2c + -9) + 96

Reorder the terms:
(-2 + c)(-7 + c) + (2c + 7)(c + -4) = c(2c + -9) + 96

Multiply (-2 + c) * (-7 + c)
(-2(-7 + c) + c(-7 + c)) + (2c + 7)(c + -4) = c(2c + -9) + 96
((-7 * -2 + c * -2) + c(-7 + c)) + (2c + 7)(c + -4) = c(2c + -9) + 96
((14 + -2c) + c(-7 + c)) + (2c + 7)(c + -4) = c(2c + -9) + 96
(14 + -2c + (-7 * c + c * c)) + (2c + 7)(c + -4) = c(2c + -9) + 96
(14 + -2c + (-7c + c2)) + (2c + 7)(c + -4) = c(2c + -9) + 96

Combine like terms: -2c + -7c = -9c
(14 + -9c + c2) + (2c + 7)(c + -4) = c(2c + -9) + 96

Reorder the terms:
14 + -9c + c2 + (7 + 2c)(c + -4) = c(2c + -9) + 96

Reorder the terms:
14 + -9c + c2 + (7 + 2c)(-4 + c) = c(2c + -9) + 96

Multiply (7 + 2c) * (-4 + c)
14 + -9c + c2 + (7(-4 + c) + 2c * (-4 + c)) = c(2c + -9) + 96
14 + -9c + c2 + ((-4 * 7 + c * 7) + 2c * (-4 + c)) = c(2c + -9) + 96
14 + -9c + c2 + ((-28 + 7c) + 2c * (-4 + c)) = c(2c + -9) + 96
14 + -9c + c2 + (-28 + 7c + (-4 * 2c + c * 2c)) = c(2c + -9) + 96
14 + -9c + c2 + (-28 + 7c + (-8c + 2c2)) = c(2c + -9) + 96

Combine like terms: 7c + -8c = -1c
14 + -9c + c2 + (-28 + -1c + 2c2) = c(2c + -9) + 96

Reorder the terms:
14 + -28 + -9c + -1c + c2 + 2c2 = c(2c + -9) + 96

Combine like terms: 14 + -28 = -14
-14 + -9c + -1c + c2 + 2c2 = c(2c + -9) + 96

Combine like terms: -9c + -1c = -10c
-14 + -10c + c2 + 2c2 = c(2c + -9) + 96

Combine like terms: c2 + 2c2 = 3c2
-14 + -10c + 3c2 = c(2c + -9) + 96

Reorder the terms:
-14 + -10c + 3c2 = c(-9 + 2c) + 96
-14 + -10c + 3c2 = (-9 * c + 2c * c) + 96
-14 + -10c + 3c2 = (-9c + 2c2) + 96

Reorder the terms:
-14 + -10c + 3c2 = 96 + -9c + 2c2

Solving
-14 + -10c + 3c2 = 96 + -9c + 2c2

Solving for variable 'c'.

Reorder the terms:
-14 + -96 + -10c + 9c + 3c2 + -2c2 = 96 + -9c + 2c2 + -96 + 9c + -2c2

Combine like terms: -14 + -96 = -110
-110 + -10c + 9c + 3c2 + -2c2 = 96 + -9c + 2c2 + -96 + 9c + -2c2

Combine like terms: -10c + 9c = -1c
-110 + -1c + 3c2 + -2c2 = 96 + -9c + 2c2 + -96 + 9c + -2c2

Combine like terms: 3c2 + -2c2 = 1c2
-110 + -1c + 1c2 = 96 + -9c + 2c2 + -96 + 9c + -2c2

Reorder the terms:
-110 + -1c + 1c2 = 96 + -96 + -9c + 9c + 2c2 + -2c2

Combine like terms: 96 + -96 = 0
-110 + -1c + 1c2 = 0 + -9c + 9c + 2c2 + -2c2
-110 + -1c + 1c2 = -9c + 9c + 2c2 + -2c2

Combine like terms: -9c + 9c = 0
-110 + -1c + 1c2 = 0 + 2c2 + -2c2
-110 + -1c + 1c2 = 2c2 + -2c2

Combine like terms: 2c2 + -2c2 = 0
-110 + -1c + 1c2 = 0

Factor a trinomial.
(-10 + -1c)(11 + -1c) = 0

Subproblem 1

Set the factor '(-10 + -1c)' equal to zero and attempt to solve: Simplifying -10 + -1c = 0 Solving -10 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1c = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1c = 0 + 10 -1c = 0 + 10 Combine like terms: 0 + 10 = 10 -1c = 10 Divide each side by '-1'. c = -10 Simplifying c = -10

Subproblem 2

Set the factor '(11 + -1c)' equal to zero and attempt to solve: Simplifying 11 + -1c = 0 Solving 11 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1c = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1c = 0 + -11 -1c = 0 + -11 Combine like terms: 0 + -11 = -11 -1c = -11 Divide each side by '-1'. c = 11 Simplifying c = 11

Solution

c = {-10, 11}

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