4(x+7)+3x(x+7)=0

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Solution for 4(x+7)+3x(x+7)=0 equation: 


Simplifying
4(x + 7) + 3x(x + 7) = 0

Reorder the terms:
4(7 + x) + 3x(x + 7) = 0
(7 * 4 + x * 4) + 3x(x + 7) = 0
(28 + 4x) + 3x(x + 7) = 0

Reorder the terms:
28 + 4x + 3x(7 + x) = 0
28 + 4x + (7 * 3x + x * 3x) = 0
28 + 4x + (21x + 3x2) = 0

Combine like terms: 4x + 21x = 25x
28 + 25x + 3x2 = 0

Solving
28 + 25x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + x)(4 + 3x) = 0


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

Simplifying
7 + x = 0

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

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

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

Simplifying
x = -7

Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {-7, -1.333333333}

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