700=(3x+20)(2x+10)

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Solution for 700=(3x+20)(2x+10) equation: 


Simplifying
700 = (3x + 20)(2x + 10)

Reorder the terms:
700 = (20 + 3x)(2x + 10)

Reorder the terms:
700 = (20 + 3x)(10 + 2x)

Multiply (20 + 3x) * (10 + 2x)
700 = (20(10 + 2x) + 3x * (10 + 2x))
700 = ((10 * 20 + 2x * 20) + 3x * (10 + 2x))
700 = ((200 + 40x) + 3x * (10 + 2x))
700 = (200 + 40x + (10 * 3x + 2x * 3x))
700 = (200 + 40x + (30x + 6x2))

Combine like terms: 40x + 30x = 70x
700 = (200 + 70x + 6x2)

Solving
700 = 200 + 70x + 6x2

Solving for variable 'x'.

Combine like terms: 700 + -200 = 500
500 + -70x + -6x2 = 200 + 70x + 6x2 + -200 + -70x + -6x2

Reorder the terms:
500 + -70x + -6x2 = 200 + -200 + 70x + -70x + 6x2 + -6x2

Combine like terms: 200 + -200 = 0
500 + -70x + -6x2 = 0 + 70x + -70x + 6x2 + -6x2
500 + -70x + -6x2 = 70x + -70x + 6x2 + -6x2

Combine like terms: 70x + -70x = 0
500 + -70x + -6x2 = 0 + 6x2 + -6x2
500 + -70x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
500 + -70x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(250 + -35x + -3x2) = 0

Factor a trinomial.
2((5 + -1x)(50 + 3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(50 + 3x)' equal to zero and attempt to solve:

Simplifying
50 + 3x = 0

Solving
50 + 3x = 0

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

Add '-50' to each side of the equation.
50 + -50 + 3x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + 3x = 0 + -50
3x = 0 + -50

Combine like terms: 0 + -50 = -50
3x = -50

Divide each side by '3'.
x = -16.66666667

Simplifying
x = -16.66666667
Solution
x = {5, -16.66666667}

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