200=(10+2x)(7+2x)-(7)(10)

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Solution for 200=(10+2x)(7+2x)-(7)(10) equation: 


Simplifying
200 = (10 + 2x)(7 + 2x) + -1(7)(10)

Multiply (10 + 2x) * (7 + 2x)
200 = (10(7 + 2x) + 2x * (7 + 2x)) + -1(7)(10)
200 = ((7 * 10 + 2x * 10) + 2x * (7 + 2x)) + -1(7)(10)
200 = ((70 + 20x) + 2x * (7 + 2x)) + -1(7)(10)
200 = (70 + 20x + (7 * 2x + 2x * 2x)) + -1(7)(10)
200 = (70 + 20x + (14x + 4x2)) + -1(7)(10)

Combine like terms: 20x + 14x = 34x
200 = (70 + 34x + 4x2) + -1(7)(10)

Multiply -1 * 7
200 = 70 + 34x + 4x2 + -7 * 10

Multiply -7 * 10
200 = 70 + 34x + 4x2 + -70

Reorder the terms:
200 = 70 + -70 + 34x + 4x2

Combine like terms: 70 + -70 = 0
200 = 0 + 34x + 4x2
200 = 34x + 4x2

Solving
200 = 34x + 4x2

Solving for variable 'x'.

Reorder the terms:
200 + -34x + -4x2 = 34x + -34x + 4x2 + -4x2

Combine like terms: 34x + -34x = 0
200 + -34x + -4x2 = 0 + 4x2 + -4x2
200 + -34x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
200 + -34x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(100 + -17x + -2x2) = 0

Factor a trinomial.
2((4 + -1x)(25 + 2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(25 + 2x)' equal to zero and attempt to solve:

Simplifying
25 + 2x = 0

Solving
25 + 2x = 0

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

Add '-25' to each side of the equation.
25 + -25 + 2x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 2x = 0 + -25
2x = 0 + -25

Combine like terms: 0 + -25 = -25
2x = -25

Divide each side by '2'.
x = -12.5

Simplifying
x = -12.5
Solution
x = {4, -12.5}

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