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

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


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

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

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

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

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

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

Solving for variable 'x'.

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

Reorder the terms:
90 + 2x + -4x2 = -12 + 12 + -2x + 2x + 4x2 + -4x2

Combine like terms: -12 + 12 = 0
90 + 2x + -4x2 = 0 + -2x + 2x + 4x2 + -4x2
90 + 2x + -4x2 = -2x + 2x + 4x2 + -4x2

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

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

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

Factor a trinomial.
2((5 + -1x)(9 + 2x)) = 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 '(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
Solution
x = {5, -4.5}

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