Question
$$-x\cdot4-2x\cdot2+13x\cdot5+6x\cdot3-7x\cdot3+5x\cdot5+7x\cdot4 = -x\cdot4-2x\cdot2+13x\cdot5+6x\cdot3-7x\cdot3+5x\cdot5+7x\cdot4$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} -x\cdot4-2x\cdot2+13x\cdot5+6x\cdot3-7x\cdot3+5x\cdot5+7x\cdot4 &= -x\cdot4-2x\cdot2+13x\cdot5+6x\cdot3-7x\cdot3+5x\cdot5+7x\cdot4&& \text{simplify left and right hand side} \\[1 em]-4x-4x+65x+18x-21x+25x+28x &= -4x-4x+65x+18x-21x+25x+28x&& \\[1 em]75x+32x &= 75x+32x&& \\[1 em]107x &= 107x&& \text{move the $ \color{blue}{ 107x } $ to the left side} \\[1 em]107x-107x &= 0&& \text{simplify left side} \\[1 em]107x-107x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 0 = 0 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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