2x^2-23x+100=-4x^2+22x+16

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Solution for 2x^2-23x+100=-4x^2+22x+16 equation: 


Simplifying
2x2 + -23x + 100 = -4x2 + 22x + 16

Reorder the terms:
100 + -23x + 2x2 = -4x2 + 22x + 16

Reorder the terms:
100 + -23x + 2x2 = 16 + 22x + -4x2

Solving
100 + -23x + 2x2 = 16 + 22x + -4x2

Solving for variable 'x'.

Reorder the terms:
100 + -16 + -23x + -22x + 2x2 + 4x2 = 16 + 22x + -4x2 + -16 + -22x + 4x2

Combine like terms: 100 + -16 = 84
84 + -23x + -22x + 2x2 + 4x2 = 16 + 22x + -4x2 + -16 + -22x + 4x2

Combine like terms: -23x + -22x = -45x
84 + -45x + 2x2 + 4x2 = 16 + 22x + -4x2 + -16 + -22x + 4x2

Combine like terms: 2x2 + 4x2 = 6x2
84 + -45x + 6x2 = 16 + 22x + -4x2 + -16 + -22x + 4x2

Reorder the terms:
84 + -45x + 6x2 = 16 + -16 + 22x + -22x + -4x2 + 4x2

Combine like terms: 16 + -16 = 0
84 + -45x + 6x2 = 0 + 22x + -22x + -4x2 + 4x2
84 + -45x + 6x2 = 22x + -22x + -4x2 + 4x2

Combine like terms: 22x + -22x = 0
84 + -45x + 6x2 = 0 + -4x2 + 4x2
84 + -45x + 6x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
84 + -45x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(28 + -15x + 2x2) = 0

Factor a trinomial.
3((7 + -2x)(4 + -1x)) = 0

Ignore the factor 3.

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

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {3.5, 4}

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