9x^2+7x-7=3x(x-4)

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Solution for 9x^2+7x-7=3x(x-4) equation: 


Simplifying
9x2 + 7x + -7 = 3x(x + -4)

Reorder the terms:
-7 + 7x + 9x2 = 3x(x + -4)

Reorder the terms:
-7 + 7x + 9x2 = 3x(-4 + x)
-7 + 7x + 9x2 = (-4 * 3x + x * 3x)
-7 + 7x + 9x2 = (-12x + 3x2)

Solving
-7 + 7x + 9x2 = -12x + 3x2

Solving for variable 'x'.

Reorder the terms:
-7 + 7x + 12x + 9x2 + -3x2 = -12x + 3x2 + 12x + -3x2

Combine like terms: 7x + 12x = 19x
-7 + 19x + 9x2 + -3x2 = -12x + 3x2 + 12x + -3x2

Combine like terms: 9x2 + -3x2 = 6x2
-7 + 19x + 6x2 = -12x + 3x2 + 12x + -3x2

Reorder the terms:
-7 + 19x + 6x2 = -12x + 12x + 3x2 + -3x2

Combine like terms: -12x + 12x = 0
-7 + 19x + 6x2 = 0 + 3x2 + -3x2
-7 + 19x + 6x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-7 + 19x + 6x2 = 0

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


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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-3.5, 0.3333333333}

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