Answer:
Explanation:
First, simplify both sides of the equation: [ \frac{{12}}{{90}}x(6x + 1) = \frac{{(7x - 2)x^2}}{{7}} ]
Multiply both sides by 90 to get rid of the fraction: [ 12x(6x + 1) = 10x(7x - 2) ]
Distribute on both sides: [ 72x^2 + 12x = 70x^2 - 20x ]
Move all terms to one side: [ 72x^2 + 12x - 70x^2 + 20x = 0 ] [ 2x^2 + 32x = 0 ]
Factor out the common factor of 2x: [ 2x(x + 16) = 0 ]
Set each factor equal to zero and solve for x:
(2x = 0), which gives (x = 0)
(x + 16 = 0), which gives (x = -16)
Therefore, the solutions to the equation are (x = 0) and (x = -16).