(3x-5)(2x+7)-5(x-7)=

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Solution for (3x-5)(2x+7)-5(x-7)= equation: 


Simplifying
(3x + -5)(2x + 7) + -5(x + -7) = 0

Reorder the terms:
(-5 + 3x)(2x + 7) + -5(x + -7) = 0

Reorder the terms:
(-5 + 3x)(7 + 2x) + -5(x + -7) = 0

Multiply (-5 + 3x) * (7 + 2x)
(-5(7 + 2x) + 3x * (7 + 2x)) + -5(x + -7) = 0
((7 * -5 + 2x * -5) + 3x * (7 + 2x)) + -5(x + -7) = 0
((-35 + -10x) + 3x * (7 + 2x)) + -5(x + -7) = 0
(-35 + -10x + (7 * 3x + 2x * 3x)) + -5(x + -7) = 0
(-35 + -10x + (21x + 6x2)) + -5(x + -7) = 0

Combine like terms: -10x + 21x = 11x
(-35 + 11x + 6x2) + -5(x + -7) = 0

Reorder the terms:
-35 + 11x + 6x2 + -5(-7 + x) = 0
-35 + 11x + 6x2 + (-7 * -5 + x * -5) = 0
-35 + 11x + 6x2 + (35 + -5x) = 0

Reorder the terms:
-35 + 35 + 11x + -5x + 6x2 = 0

Combine like terms: -35 + 35 = 0
0 + 11x + -5x + 6x2 = 0
11x + -5x + 6x2 = 0

Combine like terms: 11x + -5x = 6x
6x + 6x2 = 0

Solving
6x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(1 + x) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

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

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