(7q-3)(q+2)=4(q+5)-26

Solution for (7q-3)(q+2)=4(q+5)-26 equation:

Simplifying
(7q + -3)(q + 2) = 4(q + 5) + -26

Reorder the terms:
(-3 + 7q)(q + 2) = 4(q + 5) + -26

Reorder the terms:
(-3 + 7q)(2 + q) = 4(q + 5) + -26

Multiply (-3 + 7q) * (2 + q)
(-3(2 + q) + 7q * (2 + q)) = 4(q + 5) + -26
((2 * -3 + q * -3) + 7q * (2 + q)) = 4(q + 5) + -26
((-6 + -3q) + 7q * (2 + q)) = 4(q + 5) + -26
(-6 + -3q + (2 * 7q + q * 7q)) = 4(q + 5) + -26
(-6 + -3q + (14q + 7q2)) = 4(q + 5) + -26

Combine like terms: -3q + 14q = 11q
(-6 + 11q + 7q2) = 4(q + 5) + -26

Reorder the terms:
-6 + 11q + 7q2 = 4(5 + q) + -26
-6 + 11q + 7q2 = (5 * 4 + q * 4) + -26
-6 + 11q + 7q2 = (20 + 4q) + -26

Reorder the terms:
-6 + 11q + 7q2 = 20 + -26 + 4q

Combine like terms: 20 + -26 = -6
-6 + 11q + 7q2 = -6 + 4q

Add '6' to each side of the equation.
-6 + 11q + 6 + 7q2 = -6 + 6 + 4q

Reorder the terms:
-6 + 6 + 11q + 7q2 = -6 + 6 + 4q

Combine like terms: -6 + 6 = 0
0 + 11q + 7q2 = -6 + 6 + 4q
11q + 7q2 = -6 + 6 + 4q

Combine like terms: -6 + 6 = 0
11q + 7q2 = 0 + 4q
11q + 7q2 = 4q

Solving
11q + 7q2 = 4q

Solving for variable 'q'.

Reorder the terms:
11q + -4q + 7q2 = 4q + -4q

Combine like terms: 11q + -4q = 7q
7q + 7q2 = 4q + -4q

Combine like terms: 4q + -4q = 0
7q + 7q2 = 0

Factor out the Greatest Common Factor (GCF), '7q'.
7q(1 + q) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 'q' equal to zero and attempt to solve:

Simplifying
q = 0

Solving
q = 0

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

Simplifying
q = 0
Subproblem 2
Set the factor '(1 + q)' equal to zero and attempt to solve:

Simplifying
1 + q = 0

Solving
1 + q = 0

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

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

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

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

Simplifying
q = -1
Solution
q = {0, -1}