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

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Solution for x(2x+7)-3(2x+7)=0 equation:


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

Reorder the terms:
x(7 + 2x) + -3(2x + 7) = 0
(7 * x + 2x * x) + -3(2x + 7) = 0
(7x + 2x2) + -3(2x + 7) = 0

Reorder the terms:
7x + 2x2 + -3(7 + 2x) = 0
7x + 2x2 + (7 * -3 + 2x * -3) = 0
7x + 2x2 + (-21 + -6x) = 0

Reorder the terms:
-21 + 7x + -6x + 2x2 = 0

Combine like terms: 7x + -6x = 1x
-21 + 1x + 2x2 = 0

Solving
-21 + 1x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -2x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-3.5, 3}

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