0=16x^2-76x+90

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Solution for 0=16x^2-76x+90 equation: 


Simplifying
0 = 16x2 + -76x + 90

Reorder the terms:
0 = 90 + -76x + 16x2

Solving
0 = 90 + -76x + 16x2

Solving for variable 'x'.

Combine like terms: 0 + -90 = -90
-90 + 76x + -16x2 = 90 + -76x + 16x2 + -90 + 76x + -16x2

Reorder the terms:
-90 + 76x + -16x2 = 90 + -90 + -76x + 76x + 16x2 + -16x2

Combine like terms: 90 + -90 = 0
-90 + 76x + -16x2 = 0 + -76x + 76x + 16x2 + -16x2
-90 + 76x + -16x2 = -76x + 76x + 16x2 + -16x2

Combine like terms: -76x + 76x = 0
-90 + 76x + -16x2 = 0 + 16x2 + -16x2
-90 + 76x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-90 + 76x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 38x + -8x2) = 0

Factor a trinomial.
2((-5 + 2x)(9 + -4x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 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 + 2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 0 + 5
2x = 0 + 5

Combine like terms: 0 + 5 = 5
2x = 5

Divide each side by '2'.
x = 2.5

Simplifying
x = 2.5

Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {2.5, 2.25}

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