(2x+3)(2x-4)=78

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Solution for (2x+3)(2x-4)=78 equation: 


Simplifying
(2x + 3)(2x + -4) = 78

Reorder the terms:
(3 + 2x)(2x + -4) = 78

Reorder the terms:
(3 + 2x)(-4 + 2x) = 78

Multiply (3 + 2x) * (-4 + 2x)
(3(-4 + 2x) + 2x * (-4 + 2x)) = 78
((-4 * 3 + 2x * 3) + 2x * (-4 + 2x)) = 78
((-12 + 6x) + 2x * (-4 + 2x)) = 78
(-12 + 6x + (-4 * 2x + 2x * 2x)) = 78
(-12 + 6x + (-8x + 4x2)) = 78

Combine like terms: 6x + -8x = -2x
(-12 + -2x + 4x2) = 78

Solving
-12 + -2x + 4x2 = 78

Solving for variable 'x'.

Reorder the terms:
-12 + -78 + -2x + 4x2 = 78 + -78

Combine like terms: -12 + -78 = -90
-90 + -2x + 4x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-90 + -2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -1x + 2x2) = 0

Factor a trinomial.
2((-9 + -2x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

Subproblem 2
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
Solution
x = {-4.5, 5}

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