4q^2-7q=3q^2-9q+35

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Solution for 4q^2-7q=3q^2-9q+35 equation: 


Simplifying
4q2 + -7q = 3q2 + -9q + 35

Reorder the terms:
-7q + 4q2 = 3q2 + -9q + 35

Reorder the terms:
-7q + 4q2 = 35 + -9q + 3q2

Solving
-7q + 4q2 = 35 + -9q + 3q2

Solving for variable 'q'.

Reorder the terms:
-35 + -7q + 9q + 4q2 + -3q2 = 35 + -9q + 3q2 + -35 + 9q + -3q2

Combine like terms: -7q + 9q = 2q
-35 + 2q + 4q2 + -3q2 = 35 + -9q + 3q2 + -35 + 9q + -3q2

Combine like terms: 4q2 + -3q2 = 1q2
-35 + 2q + 1q2 = 35 + -9q + 3q2 + -35 + 9q + -3q2

Reorder the terms:
-35 + 2q + 1q2 = 35 + -35 + -9q + 9q + 3q2 + -3q2

Combine like terms: 35 + -35 = 0
-35 + 2q + 1q2 = 0 + -9q + 9q + 3q2 + -3q2
-35 + 2q + 1q2 = -9q + 9q + 3q2 + -3q2

Combine like terms: -9q + 9q = 0
-35 + 2q + 1q2 = 0 + 3q2 + -3q2
-35 + 2q + 1q2 = 3q2 + -3q2

Combine like terms: 3q2 + -3q2 = 0
-35 + 2q + 1q2 = 0

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


Subproblem 1
Set the factor '(-7 + -1q)' equal to zero and attempt to solve:

Simplifying
-7 + -1q = 0

Solving
-7 + -1q = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1q = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1q = 0 + 7
-1q = 0 + 7

Combine like terms: 0 + 7 = 7
-1q = 7

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

Simplifying
q = -7

Subproblem 2
Set the factor '(5 + -1q)' equal to zero and attempt to solve:

Simplifying
5 + -1q = 0

Solving
5 + -1q = 0

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

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

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

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

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

Simplifying
q = 5
Solution
q = {-7, 5}

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