2(x-7)(x+78)=

Solution for 2(x-7)(x+78)= equation:

Simplifying
2(x + -7)(x + 78) = 0

Reorder the terms:
2(-7 + x)(x + 78) = 0

Reorder the terms:
2(-7 + x)(78 + x) = 0

Multiply (-7 + x) * (78 + x)
2(-7(78 + x) + x(78 + x)) = 0
2((78 * -7 + x * -7) + x(78 + x)) = 0
2((-546 + -7x) + x(78 + x)) = 0
2(-546 + -7x + (78 * x + x * x)) = 0
2(-546 + -7x + (78x + x2)) = 0

Combine like terms: -7x + 78x = 71x
2(-546 + 71x + x2) = 0
(-546 * 2 + 71x * 2 + x2 * 2) = 0
(-1092 + 142x + 2x2) = 0

Solving
-1092 + 142x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-546 + 71x + x2) = 0

Factor a trinomial.
2((-78 + -1x)(7 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-78 + -1x)' equal to zero and attempt to solve:

Simplifying
-78 + -1x = 0

Solving
-78 + -1x = 0

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

Add '78' to each side of the equation.
-78 + 78 + -1x = 0 + 78

Combine like terms: -78 + 78 = 0
0 + -1x = 0 + 78
-1x = 0 + 78

Combine like terms: 0 + 78 = 78
-1x = 78

Divide each side by '-1'.
x = -78

Simplifying
x = -78
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-78, 7}