7x^2+42x=3x+18

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Solution for 7x^2+42x=3x+18 equation: 


Simplifying
7x2 + 42x = 3x + 18

Reorder the terms:
42x + 7x2 = 3x + 18

Reorder the terms:
42x + 7x2 = 18 + 3x

Solving
42x + 7x2 = 18 + 3x

Solving for variable 'x'.

Reorder the terms:
-18 + 42x + -3x + 7x2 = 18 + 3x + -18 + -3x

Combine like terms: 42x + -3x = 39x
-18 + 39x + 7x2 = 18 + 3x + -18 + -3x

Reorder the terms:
-18 + 39x + 7x2 = 18 + -18 + 3x + -3x

Combine like terms: 18 + -18 = 0
-18 + 39x + 7x2 = 0 + 3x + -3x
-18 + 39x + 7x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-18 + 39x + 7x2 = 0

Factor a trinomial.
(-6 + -1x)(3 + -7x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 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 + -7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7x = 0 + -3
-7x = 0 + -3

Combine like terms: 0 + -3 = -3
-7x = -3

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {-6, 0.4285714286}

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