0=(5x+7)(3x+7)

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Solution for 0=(5x+7)(3x+7) equation: 


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

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

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

Multiply (7 + 5x) * (7 + 3x)
0 = (7(7 + 3x) + 5x * (7 + 3x))
0 = ((7 * 7 + 3x * 7) + 5x * (7 + 3x))
0 = ((49 + 21x) + 5x * (7 + 3x))
0 = (49 + 21x + (7 * 5x + 3x * 5x))
0 = (49 + 21x + (35x + 15x2))

Combine like terms: 21x + 35x = 56x
0 = (49 + 56x + 15x2)

Solving
0 = 49 + 56x + 15x2

Solving for variable 'x'.

Combine like terms: 0 + -49 = -49
-49 + -56x + -15x2 = 49 + 56x + 15x2 + -49 + -56x + -15x2

Reorder the terms:
-49 + -56x + -15x2 = 49 + -49 + 56x + -56x + 15x2 + -15x2

Combine like terms: 49 + -49 = 0
-49 + -56x + -15x2 = 0 + 56x + -56x + 15x2 + -15x2
-49 + -56x + -15x2 = 56x + -56x + 15x2 + -15x2

Combine like terms: 56x + -56x = 0
-49 + -56x + -15x2 = 0 + 15x2 + -15x2
-49 + -56x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-49 + -56x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(49 + 56x + 15x2) = 0

Factor a trinomial.
-1((7 + 3x)(7 + 5x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 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 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 2
Set the factor '(7 + 5x)' equal to zero and attempt to solve:

Simplifying
7 + 5x = 0

Solving
7 + 5x = 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 + 5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5x = 0 + -7
5x = 0 + -7

Combine like terms: 0 + -7 = -7
5x = -7

Divide each side by '5'.
x = -1.4

Simplifying
x = -1.4
Solution
x = {-2.333333333, -1.4}

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