10c^2-29c-21=-2c^2+30c-35

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Solution for 10c^2-29c-21=-2c^2+30c-35 equation: 


Simplifying
10c2 + -29c + -21 = -2c2 + 30c + -35

Reorder the terms:
-21 + -29c + 10c2 = -2c2 + 30c + -35

Reorder the terms:
-21 + -29c + 10c2 = -35 + 30c + -2c2

Solving
-21 + -29c + 10c2 = -35 + 30c + -2c2

Solving for variable 'c'.

Reorder the terms:
-21 + 35 + -29c + -30c + 10c2 + 2c2 = -35 + 30c + -2c2 + 35 + -30c + 2c2

Combine like terms: -21 + 35 = 14
14 + -29c + -30c + 10c2 + 2c2 = -35 + 30c + -2c2 + 35 + -30c + 2c2

Combine like terms: -29c + -30c = -59c
14 + -59c + 10c2 + 2c2 = -35 + 30c + -2c2 + 35 + -30c + 2c2

Combine like terms: 10c2 + 2c2 = 12c2
14 + -59c + 12c2 = -35 + 30c + -2c2 + 35 + -30c + 2c2

Reorder the terms:
14 + -59c + 12c2 = -35 + 35 + 30c + -30c + -2c2 + 2c2

Combine like terms: -35 + 35 = 0
14 + -59c + 12c2 = 0 + 30c + -30c + -2c2 + 2c2
14 + -59c + 12c2 = 30c + -30c + -2c2 + 2c2

Combine like terms: 30c + -30c = 0
14 + -59c + 12c2 = 0 + -2c2 + 2c2
14 + -59c + 12c2 = -2c2 + 2c2

Combine like terms: -2c2 + 2c2 = 0
14 + -59c + 12c2 = 0

Factor a trinomial.
(1 + -4c)(14 + -3c) = 0


Subproblem 1
Set the factor '(1 + -4c)' equal to zero and attempt to solve:

Simplifying
1 + -4c = 0

Solving
1 + -4c = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4c = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4c = 0 + -1
-4c = 0 + -1

Combine like terms: 0 + -1 = -1
-4c = -1

Divide each side by '-4'.
c = 0.25

Simplifying
c = 0.25

Subproblem 2
Set the factor '(14 + -3c)' equal to zero and attempt to solve:

Simplifying
14 + -3c = 0

Solving
14 + -3c = 0

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

Add '-14' to each side of the equation.
14 + -14 + -3c = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -3c = 0 + -14
-3c = 0 + -14

Combine like terms: 0 + -14 = -14
-3c = -14

Divide each side by '-3'.
c = 4.666666667

Simplifying
c = 4.666666667
Solution
c = {0.25, 4.666666667}

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