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4\left(x^{2}+3x\right)
Factor out 4.
x\left(x+3\right)
Consider x^{2}+3x. Factor out x.
4x\left(x+3\right)
Rewrite the complete factored expression.
4x^{2}+12x=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-12±\sqrt{12^{2}}}{2\times 4}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-12±12}{2\times 4}
Take the square root of 12^{2}.
x=\frac{-12±12}{8}
Multiply 2 times 4.
x=\frac{0}{8}
Now solve the equation x=\frac{-12±12}{8} when ± is plus. Add -12 to 12.
x=0
Divide 0 by 8.
x=-\frac{24}{8}
Now solve the equation x=\frac{-12±12}{8} when ± is minus. Subtract 12 from -12.
x=-3
Divide -24 by 8.
4x^{2}+12x=4x\left(x-\left(-3\right)\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -3 for x_{2}.
4x^{2}+12x=4x\left(x+3\right)
Simplify all the expressions of the form p-\left(-q\right) to p+q.