4x(x+9)-7(x+9)=0

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Solution for 4x(x+9)-7(x+9)=0 equation: 


Simplifying
4x(x + 9) + -7(x + 9) = 0

Reorder the terms:
4x(9 + x) + -7(x + 9) = 0
(9 * 4x + x * 4x) + -7(x + 9) = 0
(36x + 4x2) + -7(x + 9) = 0

Reorder the terms:
36x + 4x2 + -7(9 + x) = 0
36x + 4x2 + (9 * -7 + x * -7) = 0
36x + 4x2 + (-63 + -7x) = 0

Reorder the terms:
-63 + 36x + -7x + 4x2 = 0

Combine like terms: 36x + -7x = 29x
-63 + 29x + 4x2 = 0

Solving
-63 + 29x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -1x)(7 + -4x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {-9, 1.75}

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