To solve the equation \( x^2 + 10x - 40 = 4x \) by factoring, we first need to rearrange the equation so that one side equals zero.
Starting with the initial equation: \[ x^2 + 10x - 40 = 4x \]
Subtract \( 4x \) from both sides: \[ x^2 + 10x - 4x - 40 = 0 \]
This simplifies to: \[ x^2 + 6x - 40 = 0 \]
Next, we will factor the quadratic equation \( x^2 + 6x - 40 \). We need to find two numbers that multiply to \(-40\) (the constant term) and add up to \(6\) (the coefficient of the linear term).
The numbers \(10\) and \(-4\) satisfy these conditions: \[ 10 \cdot (-4) = -40 \quad \text{and} \quad 10 + (-4) = 6 \]
Thus, we can factor the quadratic: \[ (x + 10)(x - 4) = 0 \]
Now, we can set each factor equal to zero:
- \( x + 10 = 0 \)
- \( x - 4 = 0 \)
Solving each equation gives:
- \( x = -10 \)
- \( x = 4 \)
Thus, the solutions are: \[ \boxed{-10} \quad \text{and} \quad \boxed{4} \]