Solve $\color{blue}{-16x^2+48x+28 = 0}$ using factoring.

$$ \color{blue}{ x_1 = -\frac{ 1 }{ 2 } }~~ \text{and}~~ \color{blue}{ x_2 = \frac{ 7 }{ 2 } } $$

First we need to factor trinomial $ \color{blue}{ -16x^2+48x+28 } $ and than we use factored form to solve an equation $ \color{blue}{ -16x^2+48x+28 = 0} $.

**Step 1:** We can simplify equation by multiplying both sides by **-1**.
After multiplying we have the following equation:

**Step 2:** Simplify equation by dividing all coefficients by 4

** Step 1:** **Identify constants $ a $ , $ b $ and $ c $.**

$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

** Step 2:** Multiply the leading coefficient $\color{blue}{ a = 4 }$ by
the constant term $\color{blue}{c = -7} $.

** Step 3:** Find out two numbers that multiply to $ a \cdot c = -28 $ and add to $ b = -12 $.

** Step 4:** All pairs of numbers with a product of $ -28 $ are:

PRODUCT = -28 | |

-1 28 | 1 -28 |

-2 14 | 2 -14 |

-4 7 | 4 -7 |

** Step 5:** Find out which factor pair sums up to $\color{blue}{ b = -12 }$

PRODUCT = -28 and SUM = -12 | |

-1 28 | 1 -28 |

-2 14 | 2 -14 |

-4 7 | 4 -7 |

** Step 6:** Replace middle term $ -12 x $ with $ 2x-14x $:

** Step 7:** Apply factoring by grouping. Factor $ 2x $ out of the first two terms
and $ -7 $ out of the last two terms.

** Step 8:** Set each factor to zero and solve equations.

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