(2x+12)(x-7)=528

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Solution for (2x+12)(x-7)=528 equation: 


Simplifying
(2x + 12)(x + -7) = 528

Reorder the terms:
(12 + 2x)(x + -7) = 528

Reorder the terms:
(12 + 2x)(-7 + x) = 528

Multiply (12 + 2x) * (-7 + x)
(12(-7 + x) + 2x * (-7 + x)) = 528
((-7 * 12 + x * 12) + 2x * (-7 + x)) = 528
((-84 + 12x) + 2x * (-7 + x)) = 528
(-84 + 12x + (-7 * 2x + x * 2x)) = 528
(-84 + 12x + (-14x + 2x2)) = 528

Combine like terms: 12x + -14x = -2x
(-84 + -2x + 2x2) = 528

Solving
-84 + -2x + 2x2 = 528

Solving for variable 'x'.

Reorder the terms:
-84 + -528 + -2x + 2x2 = 528 + -528

Combine like terms: -84 + -528 = -612
-612 + -2x + 2x2 = 528 + -528

Combine like terms: 528 + -528 = 0
-612 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-306 + -1x + x2) = 0

Factor a trinomial.
2((-17 + -1x)(18 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17

Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Solution
x = {-17, 18}

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