4x(x-5)+34=-17(x-2)

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Solution for 4x(x-5)+34=-17(x-2) equation: 


Simplifying
4x(x + -5) + 34 = -17(x + -2)

Reorder the terms:
4x(-5 + x) + 34 = -17(x + -2)
(-5 * 4x + x * 4x) + 34 = -17(x + -2)
(-20x + 4x2) + 34 = -17(x + -2)

Reorder the terms:
34 + -20x + 4x2 = -17(x + -2)

Reorder the terms:
34 + -20x + 4x2 = -17(-2 + x)
34 + -20x + 4x2 = (-2 * -17 + x * -17)
34 + -20x + 4x2 = (34 + -17x)

Add '-34' to each side of the equation.
34 + -20x + -34 + 4x2 = 34 + -34 + -17x

Reorder the terms:
34 + -34 + -20x + 4x2 = 34 + -34 + -17x

Combine like terms: 34 + -34 = 0
0 + -20x + 4x2 = 34 + -34 + -17x
-20x + 4x2 = 34 + -34 + -17x

Combine like terms: 34 + -34 = 0
-20x + 4x2 = 0 + -17x
-20x + 4x2 = -17x

Solving
-20x + 4x2 = -17x

Solving for variable 'x'.

Reorder the terms:
-20x + 17x + 4x2 = -17x + 17x

Combine like terms: -20x + 17x = -3x
-3x + 4x2 = -17x + 17x

Combine like terms: -17x + 17x = 0
-3x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + 4x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-3 + 4x)' equal to zero and attempt to solve:

Simplifying
-3 + 4x = 0

Solving
-3 + 4x = 0

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

Add '3' to each side of the equation.
-3 + 3 + 4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 4x = 0 + 3
4x = 0 + 3

Combine like terms: 0 + 3 = 3
4x = 3

Divide each side by '4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {0, 0.75}

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