5x(x-12)+17=17x+153

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Solution for 5x(x-12)+17=17x+153 equation: 


Simplifying
5x(x + -12) + 17 = 17x + 153

Reorder the terms:
5x(-12 + x) + 17 = 17x + 153
(-12 * 5x + x * 5x) + 17 = 17x + 153
(-60x + 5x2) + 17 = 17x + 153

Reorder the terms:
17 + -60x + 5x2 = 17x + 153

Reorder the terms:
17 + -60x + 5x2 = 153 + 17x

Solving
17 + -60x + 5x2 = 153 + 17x

Solving for variable 'x'.

Reorder the terms:
17 + -153 + -60x + -17x + 5x2 = 153 + 17x + -153 + -17x

Combine like terms: 17 + -153 = -136
-136 + -60x + -17x + 5x2 = 153 + 17x + -153 + -17x

Combine like terms: -60x + -17x = -77x
-136 + -77x + 5x2 = 153 + 17x + -153 + -17x

Reorder the terms:
-136 + -77x + 5x2 = 153 + -153 + 17x + -17x

Combine like terms: 153 + -153 = 0
-136 + -77x + 5x2 = 0 + 17x + -17x
-136 + -77x + 5x2 = 17x + -17x

Combine like terms: 17x + -17x = 0
-136 + -77x + 5x2 = 0

Factor a trinomial.
(-8 + -5x)(17 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -5x)' equal to zero and attempt to solve:

Simplifying
-8 + -5x = 0

Solving
-8 + -5x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -5x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5x = 0 + 8
-5x = 0 + 8

Combine like terms: 0 + 8 = 8
-5x = 8

Divide each side by '-5'.
x = -1.6

Simplifying
x = -1.6

Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {-1.6, 17}

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