7(x^2-6x+9)+5(x-3)=0

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Solution for 7(x^2-6x+9)+5(x-3)=0 equation: 


Simplifying
7(x2 + -6x + 9) + 5(x + -3) = 0

Reorder the terms:
7(9 + -6x + x2) + 5(x + -3) = 0
(9 * 7 + -6x * 7 + x2 * 7) + 5(x + -3) = 0
(63 + -42x + 7x2) + 5(x + -3) = 0

Reorder the terms:
63 + -42x + 7x2 + 5(-3 + x) = 0
63 + -42x + 7x2 + (-3 * 5 + x * 5) = 0
63 + -42x + 7x2 + (-15 + 5x) = 0

Reorder the terms:
63 + -15 + -42x + 5x + 7x2 = 0

Combine like terms: 63 + -15 = 48
48 + -42x + 5x + 7x2 = 0

Combine like terms: -42x + 5x = -37x
48 + -37x + 7x2 = 0

Solving
48 + -37x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(16 + -7x)(3 + -1x) = 0


Subproblem 1
Set the factor '(16 + -7x)' equal to zero and attempt to solve:

Simplifying
16 + -7x = 0

Solving
16 + -7x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -7x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -7x = 0 + -16
-7x = 0 + -16

Combine like terms: 0 + -16 = -16
-7x = -16

Divide each side by '-7'.
x = 2.285714286

Simplifying
x = 2.285714286

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 = {2.285714286, 3}

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